id	sid	tid	token	lemma	pos
ejpam-3703	1	1	european	european	PROPN
ejpam-3703	1	2	journal	journal	PROPN
ejpam-3703	1	3	of	of	ADP
ejpam-3703	1	4	pure	pure	ADJ
ejpam-3703	1	5	and	and	CCONJ
ejpam-3703	1	6	applied	apply	VERB
ejpam-3703	1	7	mathematics	mathematic	NOUN
ejpam-3703	1	8	vol	vol	NOUN
ejpam-3703	1	9	.	.	PROPN
ejpam-3703	2	1	13	13	NUM
ejpam-3703	2	2	,	,	PUNCT
ejpam-3703	2	3	no	no	INTJ
ejpam-3703	2	4	.	.	NOUN
ejpam-3703	2	5	2	2	NUM
ejpam-3703	2	6	,	,	PUNCT
ejpam-3703	2	7	2020	2020	NUM
ejpam-3703	2	8	,	,	PUNCT
ejpam-3703	2	9	346	346	NUM
ejpam-3703	2	10	-	-	SYM
ejpam-3703	2	11	350	350	NUM
ejpam-3703	2	12	issn	issn	PROPN
ejpam-3703	2	13	1307	1307	NUM
ejpam-3703	2	14	-	-	SYM
ejpam-3703	2	15	5543	5543	NUM
ejpam-3703	2	16	–	–	PUNCT
ejpam-3703	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3703	2	18	published	publish	VERB
ejpam-3703	2	19	by	by	ADP
ejpam-3703	2	20	new	new	PROPN
ejpam-3703	2	21	york	york	PROPN
ejpam-3703	2	22	business	business	PROPN
ejpam-3703	2	23	global	global	PROPN
ejpam-3703	2	24	on	on	ADP
ejpam-3703	2	25	regular	regular	ADJ
ejpam-3703	2	26	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	2	27	niovi	niovi	NOUN
ejpam-3703	2	28	kehayopulu	kehayopulu	ADJ
ejpam-3703	2	29	abstract	abstract	NOUN
ejpam-3703	2	30	.	.	PUNCT
ejpam-3703	3	1	it	it	PRON
ejpam-3703	3	2	is	be	AUX
ejpam-3703	3	3	shown	show	VERB
ejpam-3703	3	4	that	that	SCONJ
ejpam-3703	3	5	an	an	DET
ejpam-3703	3	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	3	7	(	(	PUNCT
ejpam-3703	3	8	s	s	NOUN
ejpam-3703	3	9	,	,	PUNCT
ejpam-3703	3	10	◦	◦	NOUN
ejpam-3703	3	11	)	)	PUNCT
ejpam-3703	3	12	is	be	AUX
ejpam-3703	3	13	regular	regular	ADJ
ejpam-3703	3	14	if	if	SCONJ
ejpam-3703	3	15	and	and	CCONJ
ejpam-3703	3	16	only	only	ADV
ejpam-3703	3	17	if	if	SCONJ
ejpam-3703	3	18	the	the	DET
ejpam-3703	3	19	set	set	NOUN
ejpam-3703	3	20	of	of	ADP
ejpam-3703	3	21	all	all	DET
ejpam-3703	3	22	quasiideals	quasiideal	NOUN
ejpam-3703	3	23	of	of	ADP
ejpam-3703	3	24	s	s	PRON
ejpam-3703	3	25	with	with	ADP
ejpam-3703	3	26	the	the	DET
ejpam-3703	3	27	operation	operation	NOUN
ejpam-3703	3	28	“	"	PUNCT
ejpam-3703	3	29	∗	∗	NOUN
ejpam-3703	3	30	”	"	PUNCT
ejpam-3703	3	31	is	be	AUX
ejpam-3703	3	32	a	a	DET
ejpam-3703	3	33	von	von	PROPN
ejpam-3703	3	34	neumann	neumann	PROPN
ejpam-3703	3	35	regular	regular	PROPN
ejpam-3703	3	36	semigroup	semigroup	PROPN
ejpam-3703	3	37	.	.	PUNCT
ejpam-3703	4	1	it	it	PRON
ejpam-3703	4	2	is	be	AUX
ejpam-3703	4	3	both	both	CCONJ
ejpam-3703	4	4	regular	regular	ADJ
ejpam-3703	4	5	and	and	CCONJ
ejpam-3703	4	6	intra	intra	ADJ
ejpam-3703	4	7	-	-	ADJ
ejpam-3703	4	8	regular	regular	ADJ
ejpam-3703	4	9	if	if	SCONJ
ejpam-3703	5	1	and	and	CCONJ
ejpam-3703	5	2	only	only	ADV
ejpam-3703	5	3	if	if	SCONJ
ejpam-3703	5	4	the	the	DET
ejpam-3703	5	5	set	set	NOUN
ejpam-3703	5	6	of	of	ADP
ejpam-3703	5	7	all	all	DET
ejpam-3703	5	8	quasi	quasi	NOUN
ejpam-3703	5	9	-	-	NOUN
ejpam-3703	5	10	ideals	ideal	NOUN
ejpam-3703	5	11	of	of	ADP
ejpam-3703	5	12	s	s	NOUN
ejpam-3703	5	13	with	with	ADP
ejpam-3703	5	14	the	the	DET
ejpam-3703	5	15	operation	operation	NOUN
ejpam-3703	5	16	“	"	PUNCT
ejpam-3703	5	17	∗	∗	NOUN
ejpam-3703	5	18	”	"	PUNCT
ejpam-3703	5	19	is	be	AUX
ejpam-3703	5	20	a	a	DET
ejpam-3703	5	21	band	band	NOUN
ejpam-3703	5	22	.	.	PUNCT
ejpam-3703	6	1	2020	2020	NUM
ejpam-3703	6	2	mathematics	mathematic	NOUN
ejpam-3703	6	3	subject	subject	NOUN
ejpam-3703	6	4	classifications	classification	NOUN
ejpam-3703	6	5	:	:	PUNCT
ejpam-3703	6	6	20m99	20m99	NUM
ejpam-3703	6	7	,	,	PUNCT
ejpam-3703	6	8	06f05	06f05	NOUN
ejpam-3703	6	9	key	key	ADJ
ejpam-3703	6	10	words	word	NOUN
ejpam-3703	6	11	and	and	CCONJ
ejpam-3703	6	12	phrases	phrase	NOUN
ejpam-3703	6	13	:	:	PUNCT
ejpam-3703	6	14	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	6	15	,	,	PUNCT
ejpam-3703	6	16	regular	regular	ADJ
ejpam-3703	6	17	,	,	PUNCT
ejpam-3703	6	18	intra	intra	ADJ
ejpam-3703	6	19	-	-	ADJ
ejpam-3703	6	20	regular	regular	ADJ
ejpam-3703	6	21	,	,	PUNCT
ejpam-3703	6	22	right	right	INTJ
ejpam-3703	6	23	(	(	PUNCT
ejpam-3703	6	24	left	left	ADJ
ejpam-3703	6	25	)	)	PUNCT
ejpam-3703	6	26	ideal	ideal	ADJ
ejpam-3703	6	27	,	,	PUNCT
ejpam-3703	6	28	quasi	quasi	ADJ
ejpam-3703	6	29	-	-	ADJ
ejpam-3703	6	30	ideal	ideal	ADJ
ejpam-3703	6	31	,	,	PUNCT
ejpam-3703	6	32	band	band	NOUN
ejpam-3703	6	33	it	it	PRON
ejpam-3703	6	34	has	have	AUX
ejpam-3703	6	35	been	be	AUX
ejpam-3703	6	36	shown	show	VERB
ejpam-3703	6	37	in	in	ADP
ejpam-3703	6	38	semigroup	semigroup	PROPN
ejpam-3703	6	39	forum	forum	PROPN
ejpam-3703	7	1	[	[	X
ejpam-3703	7	2	2	2	X
ejpam-3703	7	3	]	]	PUNCT
ejpam-3703	7	4	that	that	SCONJ
ejpam-3703	7	5	an	an	DET
ejpam-3703	7	6	le	le	X
ejpam-3703	7	7	-	-	NOUN
ejpam-3703	7	8	semigroup	semigroup	PROPN
ejpam-3703	7	9	(	(	PUNCT
ejpam-3703	7	10	s	s	PROPN
ejpam-3703	7	11	,	,	PUNCT
ejpam-3703	7	12	·	·	PUNCT
ejpam-3703	7	13	,	,	PUNCT
ejpam-3703	7	14	≤	≤	NUM
ejpam-3703	7	15	)	)	PUNCT
ejpam-3703	7	16	is	be	AUX
ejpam-3703	7	17	regular	regular	ADJ
ejpam-3703	7	18	if	if	SCONJ
ejpam-3703	7	19	and	and	CCONJ
ejpam-3703	7	20	only	only	ADV
ejpam-3703	7	21	if	if	SCONJ
ejpam-3703	7	22	the	the	DET
ejpam-3703	7	23	set	set	NOUN
ejpam-3703	7	24	q	q	NOUN
ejpam-3703	7	25	of	of	ADP
ejpam-3703	7	26	all	all	DET
ejpam-3703	7	27	quasi	quasi	ADJ
ejpam-3703	7	28	-	-	ADJ
ejpam-3703	7	29	ideal	ideal	ADJ
ejpam-3703	7	30	elements	element	NOUN
ejpam-3703	7	31	of	of	ADP
ejpam-3703	7	32	s	s	NOUN
ejpam-3703	7	33	with	with	ADP
ejpam-3703	7	34	the	the	DET
ejpam-3703	7	35	multiplication	multiplication	NOUN
ejpam-3703	7	36	“	"	PUNCT
ejpam-3703	7	37	·	·	PUNCT
ejpam-3703	7	38	”	"	PUNCT
ejpam-3703	7	39	of	of	ADP
ejpam-3703	7	40	s	s	PROPN
ejpam-3703	7	41	is	be	AUX
ejpam-3703	7	42	a	a	DET
ejpam-3703	7	43	von	von	PROPN
ejpam-3703	7	44	neumann	neumann	PROPN
ejpam-3703	7	45	regular	regular	PROPN
ejpam-3703	7	46	semigroup	semigroup	PROPN
ejpam-3703	7	47	.	.	PUNCT
ejpam-3703	8	1	moreover	moreover	ADV
ejpam-3703	8	2	,	,	PUNCT
ejpam-3703	8	3	it	it	PRON
ejpam-3703	8	4	has	have	AUX
ejpam-3703	8	5	been	be	AUX
ejpam-3703	8	6	proved	prove	VERB
ejpam-3703	8	7	that	that	SCONJ
ejpam-3703	8	8	if	if	SCONJ
ejpam-3703	8	9	s	s	NOUN
ejpam-3703	8	10	is	be	AUX
ejpam-3703	8	11	both	both	PRON
ejpam-3703	8	12	regular	regular	ADJ
ejpam-3703	8	13	and	and	CCONJ
ejpam-3703	8	14	intra	intra	ADJ
ejpam-3703	8	15	-	-	ADJ
ejpam-3703	8	16	regular	regular	ADJ
ejpam-3703	8	17	,	,	PUNCT
ejpam-3703	8	18	then	then	ADV
ejpam-3703	8	19	(	(	PUNCT
ejpam-3703	8	20	q	q	NOUN
ejpam-3703	8	21	,	,	PUNCT
ejpam-3703	8	22	·	·	PUNCT
ejpam-3703	8	23	)	)	PUNCT
ejpam-3703	8	24	is	be	AUX
ejpam-3703	8	25	a	a	DET
ejpam-3703	8	26	band	band	NOUN
ejpam-3703	8	27	.	.	PUNCT
ejpam-3703	9	1	“	"	PUNCT
ejpam-3703	9	2	conversely	conversely	ADV
ejpam-3703	9	3	”	"	PUNCT
ejpam-3703	9	4	,	,	PUNCT
ejpam-3703	9	5	if	if	SCONJ
ejpam-3703	9	6	the	the	DET
ejpam-3703	9	7	quasi	quasi	ADJ
ejpam-3703	9	8	-	-	ADJ
ejpam-3703	9	9	ideal	ideal	ADJ
ejpam-3703	9	10	elements	element	NOUN
ejpam-3703	9	11	of	of	ADP
ejpam-3703	9	12	s	s	NOUN
ejpam-3703	9	13	are	be	AUX
ejpam-3703	9	14	idempotent	idempotent	ADJ
ejpam-3703	9	15	,	,	PUNCT
ejpam-3703	9	16	then	then	ADV
ejpam-3703	9	17	s	s	VERB
ejpam-3703	9	18	is	be	AUX
ejpam-3703	9	19	both	both	PRON
ejpam-3703	9	20	regular	regular	ADJ
ejpam-3703	9	21	and	and	CCONJ
ejpam-3703	9	22	intra	intra	ADJ
ejpam-3703	9	23	-	-	ADJ
ejpam-3703	9	24	regular	regular	ADJ
ejpam-3703	9	25	.	.	PUNCT
ejpam-3703	10	1	as	as	ADP
ejpam-3703	10	2	a	a	DET
ejpam-3703	10	3	consequence	consequence	NOUN
ejpam-3703	10	4	,	,	PUNCT
ejpam-3703	10	5	an	an	DET
ejpam-3703	10	6	le	le	X
ejpam-3703	10	7	-	-	NOUN
ejpam-3703	10	8	semigroup	semigroup	PROPN
ejpam-3703	10	9	s	s	VERB
ejpam-3703	10	10	is	be	AUX
ejpam-3703	10	11	both	both	PRON
ejpam-3703	10	12	regular	regular	ADJ
ejpam-3703	10	13	and	and	CCONJ
ejpam-3703	10	14	intra	intra	ADJ
ejpam-3703	10	15	-	-	ADJ
ejpam-3703	10	16	regular	regular	ADJ
ejpam-3703	10	17	if	if	SCONJ
ejpam-3703	10	18	and	and	CCONJ
ejpam-3703	10	19	only	only	ADV
ejpam-3703	10	20	if	if	SCONJ
ejpam-3703	10	21	(	(	PUNCT
ejpam-3703	10	22	q	q	NOUN
ejpam-3703	10	23	,	,	PUNCT
ejpam-3703	10	24	·	·	PUNCT
ejpam-3703	10	25	)	)	PUNCT
ejpam-3703	10	26	is	be	AUX
ejpam-3703	10	27	a	a	DET
ejpam-3703	10	28	band	band	NOUN
ejpam-3703	10	29	.	.	PUNCT
ejpam-3703	11	1	as	as	ADP
ejpam-3703	11	2	an	an	DET
ejpam-3703	11	3	example	example	NOUN
ejpam-3703	11	4	to	to	ADP
ejpam-3703	11	5	the	the	DET
ejpam-3703	11	6	paper	paper	NOUN
ejpam-3703	11	7	in	in	ADP
ejpam-3703	11	8	turkish	turkish	ADJ
ejpam-3703	11	9	j.	j.	PROPN
ejpam-3703	11	10	math	math	PROPN
ejpam-3703	11	11	.	.	PUNCT
ejpam-3703	12	1	[	[	X
ejpam-3703	12	2	7	7	NUM
ejpam-3703	12	3	]	]	PUNCT
ejpam-3703	12	4	,	,	PUNCT
ejpam-3703	12	5	we	we	PRON
ejpam-3703	12	6	examine	examine	VERB
ejpam-3703	12	7	the	the	DET
ejpam-3703	12	8	above	above	ADJ
ejpam-3703	12	9	results	result	NOUN
ejpam-3703	12	10	on	on	ADP
ejpam-3703	12	11	lattice	lattice	NOUN
ejpam-3703	12	12	ordered	order	VERB
ejpam-3703	12	13	semigroups	semigroup	NOUN
ejpam-3703	12	14	in	in	ADP
ejpam-3703	12	15	case	case	NOUN
ejpam-3703	12	16	of	of	ADP
ejpam-3703	12	17	an	an	DET
ejpam-3703	12	18	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	12	19	.	.	PUNCT
ejpam-3703	13	1	an	an	DET
ejpam-3703	13	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	13	3	(	(	PUNCT
ejpam-3703	13	4	s	s	NOUN
ejpam-3703	13	5	,	,	PUNCT
ejpam-3703	13	6	◦	◦	NOUN
ejpam-3703	13	7	)	)	PUNCT
ejpam-3703	13	8	is	be	AUX
ejpam-3703	13	9	called	call	VERB
ejpam-3703	13	10	regular	regular	ADV
ejpam-3703	13	11	if	if	SCONJ
ejpam-3703	13	12	for	for	SCONJ
ejpam-3703	13	13	every	every	DET
ejpam-3703	13	14	a	a	DET
ejpam-3703	13	15	∈	∈	NOUN
ejpam-3703	13	16	s	s	VERB
ejpam-3703	13	17	there	there	PRON
ejpam-3703	13	18	exists	exist	VERB
ejpam-3703	13	19	x	x	X
ejpam-3703	13	20	∈	∈	NOUN
ejpam-3703	13	21	s	s	VERB
ejpam-3703	13	22	such	such	ADJ
ejpam-3703	13	23	that	that	SCONJ
ejpam-3703	13	24	a	a	DET
ejpam-3703	13	25	∈	∈	NOUN
ejpam-3703	13	26	(	(	PUNCT
ejpam-3703	13	27	a	a	DET
ejpam-3703	13	28	◦	◦	NOUN
ejpam-3703	13	29	x	x	SYM
ejpam-3703	13	30	)	)	PUNCT
ejpam-3703	13	31	∗	∗	NOUN
ejpam-3703	13	32	{	{	PUNCT
ejpam-3703	13	33	a	a	NOUN
ejpam-3703	13	34	}	}	PUNCT
ejpam-3703	13	35	;	;	PUNCT
ejpam-3703	13	36	that	that	PRON
ejpam-3703	13	37	is	is	ADV
ejpam-3703	13	38	,	,	PUNCT
ejpam-3703	13	39	for	for	SCONJ
ejpam-3703	13	40	every	every	DET
ejpam-3703	13	41	a	a	DET
ejpam-3703	13	42	∈	∈	NOUN
ejpam-3703	13	43	s	s	VERB
ejpam-3703	13	44	there	there	PRON
ejpam-3703	13	45	exists	exist	VERB
ejpam-3703	13	46	y	y	PROPN
ejpam-3703	13	47	∈	∈	PROPN
ejpam-3703	13	48	a	a	DET
ejpam-3703	13	49	◦	◦	NOUN
ejpam-3703	13	50	x	x	SYM
ejpam-3703	13	51	such	such	ADJ
ejpam-3703	13	52	that	that	SCONJ
ejpam-3703	13	53	a	a	DET
ejpam-3703	13	54	∈	∈	PROPN
ejpam-3703	13	55	y	y	PROPN
ejpam-3703	13	56	◦	◦	NOUN
ejpam-3703	13	57	a.	a.	NOUN
ejpam-3703	13	58	it	it	PRON
ejpam-3703	13	59	is	be	AUX
ejpam-3703	13	60	called	call	VERB
ejpam-3703	13	61	intra	intra	ADJ
ejpam-3703	13	62	-	-	ADJ
ejpam-3703	13	63	regular	regular	ADJ
ejpam-3703	13	64	if	if	SCONJ
ejpam-3703	13	65	for	for	SCONJ
ejpam-3703	13	66	every	every	DET
ejpam-3703	13	67	a	a	DET
ejpam-3703	13	68	∈	∈	NOUN
ejpam-3703	13	69	s	s	VERB
ejpam-3703	13	70	there	there	PRON
ejpam-3703	13	71	exist	exist	VERB
ejpam-3703	13	72	x	x	NOUN
ejpam-3703	13	73	,	,	PUNCT
ejpam-3703	13	74	y	y	PROPN
ejpam-3703	13	75	∈	∈	PROPN
ejpam-3703	13	76	s	s	VERB
ejpam-3703	13	77	such	such	ADJ
ejpam-3703	13	78	that	that	SCONJ
ejpam-3703	13	79	a	a	DET
ejpam-3703	13	80	∈	∈	NOUN
ejpam-3703	13	81	(	(	PUNCT
ejpam-3703	13	82	x	x	SYM
ejpam-3703	13	83	◦	◦	VERB
ejpam-3703	13	84	a	a	X
ejpam-3703	13	85	)	)	PUNCT
ejpam-3703	13	86	∗	∗	NOUN
ejpam-3703	13	87	(	(	PUNCT
ejpam-3703	13	88	a	a	DET
ejpam-3703	13	89	◦	◦	NOUN
ejpam-3703	13	90	y	y	PROPN
ejpam-3703	13	91	)	)	PUNCT
ejpam-3703	13	92	;	;	PUNCT
ejpam-3703	13	93	that	that	PRON
ejpam-3703	13	94	is	is	ADV
ejpam-3703	13	95	,	,	PUNCT
ejpam-3703	13	96	for	for	ADP
ejpam-3703	13	97	every	every	DET
ejpam-3703	13	98	a	a	DET
ejpam-3703	13	99	∈	∈	NOUN
ejpam-3703	13	100	s	s	VERB
ejpam-3703	13	101	there	there	PRON
ejpam-3703	13	102	exist	exist	VERB
ejpam-3703	13	103	x	x	NOUN
ejpam-3703	13	104	,	,	PUNCT
ejpam-3703	13	105	y	y	PROPN
ejpam-3703	13	106	∈	∈	PROPN
ejpam-3703	13	107	s	s	PROPN
ejpam-3703	13	108	,	,	PUNCT
ejpam-3703	13	109	u	u	PROPN
ejpam-3703	13	110	∈	∈	PROPN
ejpam-3703	13	111	x	x	PUNCT
ejpam-3703	13	112	◦	◦	VERB
ejpam-3703	13	113	a	a	PRON
ejpam-3703	13	114	and	and	CCONJ
ejpam-3703	13	115	v	v	ADP
ejpam-3703	13	116	∈	∈	PROPN
ejpam-3703	13	117	a	a	DET
ejpam-3703	13	118	◦	◦	NOUN
ejpam-3703	13	119	y	y	PRON
ejpam-3703	13	120	such	such	ADJ
ejpam-3703	13	121	that	that	SCONJ
ejpam-3703	13	122	a	a	DET
ejpam-3703	13	123	∈	∈	PROPN
ejpam-3703	13	124	u	u	NOUN
ejpam-3703	13	125	◦	◦	NOUN
ejpam-3703	13	126	v.	v.	ADP
ejpam-3703	13	127	a	a	DET
ejpam-3703	13	128	subset	subset	NOUN
ejpam-3703	13	129	a	a	PRON
ejpam-3703	13	130	of	of	ADP
ejpam-3703	13	131	an	an	DET
ejpam-3703	13	132	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	13	133	(	(	PUNCT
ejpam-3703	13	134	s	s	NOUN
ejpam-3703	13	135	,	,	PUNCT
ejpam-3703	13	136	◦	◦	NOUN
ejpam-3703	13	137	)	)	PUNCT
ejpam-3703	13	138	is	be	AUX
ejpam-3703	13	139	called	call	VERB
ejpam-3703	13	140	idempotent	idempotent	ADJ
ejpam-3703	13	141	if	if	SCONJ
ejpam-3703	13	142	a	a	DET
ejpam-3703	13	143	∗	∗	NOUN
ejpam-3703	13	144	a	a	DET
ejpam-3703	13	145	=	=	NOUN
ejpam-3703	13	146	a.	a.	NOUN
ejpam-3703	13	147	for	for	ADP
ejpam-3703	13	148	notations	notation	NOUN
ejpam-3703	13	149	and	and	CCONJ
ejpam-3703	13	150	definitions	definition	NOUN
ejpam-3703	13	151	not	not	PART
ejpam-3703	13	152	given	give	VERB
ejpam-3703	13	153	in	in	ADP
ejpam-3703	13	154	the	the	DET
ejpam-3703	13	155	present	present	ADJ
ejpam-3703	13	156	paper	paper	NOUN
ejpam-3703	13	157	we	we	PRON
ejpam-3703	13	158	refer	refer	VERB
ejpam-3703	13	159	to	to	ADP
ejpam-3703	13	160	[	[	X
ejpam-3703	13	161	7	7	NUM
ejpam-3703	13	162	]	]	PUNCT
ejpam-3703	13	163	.	.	PUNCT
ejpam-3703	14	1	lemma	lemma	PROPN
ejpam-3703	14	2	1	1	NUM
ejpam-3703	15	1	[	[	X
ejpam-3703	15	2	3	3	NUM
ejpam-3703	15	3	]	]	X
ejpam-3703	15	4	let	let	VERB
ejpam-3703	15	5	(	(	PUNCT
ejpam-3703	15	6	s	s	NOUN
ejpam-3703	15	7	,	,	PUNCT
ejpam-3703	15	8	◦	◦	NOUN
ejpam-3703	15	9	)	)	PUNCT
ejpam-3703	15	10	be	be	VERB
ejpam-3703	15	11	an	an	DET
ejpam-3703	15	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	15	13	.	.	PUNCT
ejpam-3703	16	1	if	if	SCONJ
ejpam-3703	16	2	s	s	NOUN
ejpam-3703	16	3	is	be	AUX
ejpam-3703	16	4	regular	regular	ADJ
ejpam-3703	16	5	,	,	PUNCT
ejpam-3703	16	6	then	then	ADV
ejpam-3703	16	7	the	the	DET
ejpam-3703	16	8	right	right	ADJ
ejpam-3703	16	9	ideals	ideal	NOUN
ejpam-3703	16	10	and	and	CCONJ
ejpam-3703	16	11	the	the	DET
ejpam-3703	16	12	left	left	ADJ
ejpam-3703	16	13	ideals	ideal	NOUN
ejpam-3703	16	14	of	of	ADP
ejpam-3703	16	15	s	s	PRON
ejpam-3703	16	16	are	be	AUX
ejpam-3703	16	17	idempotent	idempotent	ADJ
ejpam-3703	16	18	and	and	CCONJ
ejpam-3703	16	19	for	for	ADP
ejpam-3703	16	20	every	every	DET
ejpam-3703	16	21	right	right	ADJ
ejpam-3703	16	22	ideal	ideal	NOUN
ejpam-3703	16	23	a	a	PRON
ejpam-3703	16	24	and	and	CCONJ
ejpam-3703	16	25	every	every	PRON
ejpam-3703	16	26	left	leave	VERB
ejpam-3703	16	27	ideal	ideal	PROPN
ejpam-3703	16	28	b	b	PROPN
ejpam-3703	16	29	of	of	ADP
ejpam-3703	16	30	s	s	PROPN
ejpam-3703	16	31	,	,	PUNCT
ejpam-3703	16	32	the	the	DET
ejpam-3703	16	33	product	product	NOUN
ejpam-3703	16	34	a	a	DET
ejpam-3703	16	35	∗b	∗b	PROPN
ejpam-3703	16	36	is	be	AUX
ejpam-3703	16	37	a	a	DET
ejpam-3703	16	38	quasi	quasi	NOUN
ejpam-3703	16	39	-	-	NOUN
ejpam-3703	16	40	ideal	ideal	NOUN
ejpam-3703	16	41	of	of	ADP
ejpam-3703	16	42	s.	s.	PROPN
ejpam-3703	16	43	lemma	lemma	PROPN
ejpam-3703	16	44	2	2	NUM
ejpam-3703	17	1	[	[	X
ejpam-3703	17	2	4	4	NUM
ejpam-3703	17	3	,	,	PUNCT
ejpam-3703	17	4	5	5	NUM
ejpam-3703	17	5	]	]	PUNCT
ejpam-3703	17	6	an	an	DET
ejpam-3703	17	7	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	17	8	(	(	PUNCT
ejpam-3703	17	9	s	s	NOUN
ejpam-3703	17	10	,	,	PUNCT
ejpam-3703	17	11	◦	◦	NOUN
ejpam-3703	17	12	)	)	PUNCT
ejpam-3703	17	13	is	be	AUX
ejpam-3703	17	14	regular	regular	ADJ
ejpam-3703	17	15	if	if	SCONJ
ejpam-3703	17	16	and	and	CCONJ
ejpam-3703	17	17	only	only	ADV
ejpam-3703	17	18	if	if	SCONJ
ejpam-3703	17	19	,	,	PUNCT
ejpam-3703	17	20	for	for	ADP
ejpam-3703	17	21	any	any	DET
ejpam-3703	17	22	nonempty	nonempty	NOUN
ejpam-3703	17	23	subset	subset	VERB
ejpam-3703	17	24	a	a	PRON
ejpam-3703	17	25	of	of	ADP
ejpam-3703	17	26	s	s	PROPN
ejpam-3703	17	27	,	,	PUNCT
ejpam-3703	17	28	we	we	PRON
ejpam-3703	17	29	have	have	VERB
ejpam-3703	17	30	a	a	DET
ejpam-3703	17	31	⊆	⊆	NUM
ejpam-3703	17	32	a	a	DET
ejpam-3703	17	33	∗	∗	NOUN
ejpam-3703	17	34	s	s	NOUN
ejpam-3703	17	35	∗a	∗a	PROPN
ejpam-3703	17	36	.	.	PUNCT
ejpam-3703	18	1	lemma	lemma	PROPN
ejpam-3703	18	2	3	3	NUM
ejpam-3703	18	3	let	let	VERB
ejpam-3703	18	4	(	(	PUNCT
ejpam-3703	18	5	s	s	NOUN
ejpam-3703	18	6	,	,	PUNCT
ejpam-3703	18	7	◦	◦	NOUN
ejpam-3703	18	8	)	)	PUNCT
ejpam-3703	18	9	be	be	VERB
ejpam-3703	18	10	an	an	DET
ejpam-3703	18	11	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	18	12	,	,	PUNCT
ejpam-3703	18	13	a	a	DET
ejpam-3703	18	14	a	a	DET
ejpam-3703	18	15	right	right	ADJ
ejpam-3703	18	16	ideal	ideal	NOUN
ejpam-3703	18	17	and	and	CCONJ
ejpam-3703	18	18	b	b	DET
ejpam-3703	18	19	a	a	DET
ejpam-3703	18	20	left	left	ADJ
ejpam-3703	18	21	ideal	ideal	NOUN
ejpam-3703	18	22	of	of	ADP
ejpam-3703	18	23	s.	s.	PROPN
ejpam-3703	18	24	then	then	ADV
ejpam-3703	18	25	the	the	DET
ejpam-3703	18	26	intersection	intersection	NOUN
ejpam-3703	18	27	a	a	DET
ejpam-3703	18	28	∩b	∩b	NOUN
ejpam-3703	18	29	is	be	AUX
ejpam-3703	18	30	a	a	DET
ejpam-3703	18	31	quasi	quasi	NOUN
ejpam-3703	18	32	-	-	NOUN
ejpam-3703	18	33	ideal	ideal	NOUN
ejpam-3703	18	34	of	of	ADP
ejpam-3703	18	35	s.	s.	PROPN
ejpam-3703	18	36	doi	doi	PROPN
ejpam-3703	18	37	:	:	PUNCT
ejpam-3703	18	38	https://doi.org/10.29020/nybg.ejpam.v13i2.3703	https://doi.org/10.29020/nybg.ejpam.v13i2.3703	ADJ
ejpam-3703	18	39	email	email	NOUN
ejpam-3703	18	40	address	address	NOUN
ejpam-3703	18	41	:	:	PUNCT
ejpam-3703	18	42	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3703	18	43	(	(	PUNCT
ejpam-3703	18	44	n.	n.	PROPN
ejpam-3703	18	45	kehayopulu	kehayopulu	PROPN
ejpam-3703	18	46	)	)	PUNCT
ejpam-3703	18	47	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3703	19	1	346	346	NUM
ejpam-3703	19	2	c	c	X
ejpam-3703	19	3	©	©	NOUN
ejpam-3703	19	4	2020	2020	NUM
ejpam-3703	19	5	ejpam	ejpam	VERB
ejpam-3703	19	6	all	all	DET
ejpam-3703	19	7	rights	right	NOUN
ejpam-3703	19	8	reserved	reserve	VERB
ejpam-3703	19	9	.	.	PUNCT
ejpam-3703	20	1	n.	n.	PROPN
ejpam-3703	20	2	kehayopulu	kehayopulu	PROPN
ejpam-3703	20	3	/	/	SYM
ejpam-3703	20	4	eur	eur	PROPN
ejpam-3703	20	5	.	.	PUNCT
ejpam-3703	21	1	j.	j.	PROPN
ejpam-3703	21	2	pure	pure	PROPN
ejpam-3703	21	3	appl	appl	PROPN
ejpam-3703	21	4	.	.	PROPN
ejpam-3703	21	5	math	math	PROPN
ejpam-3703	21	6	,	,	PUNCT
ejpam-3703	21	7	13	13	NUM
ejpam-3703	21	8	(	(	PUNCT
ejpam-3703	21	9	2	2	NUM
ejpam-3703	21	10	)	)	PUNCT
ejpam-3703	21	11	(	(	PUNCT
ejpam-3703	21	12	2020	2020	NUM
ejpam-3703	21	13	)	)	PUNCT
ejpam-3703	21	14	,	,	PUNCT
ejpam-3703	21	15	346	346	NUM
ejpam-3703	21	16	-	-	SYM
ejpam-3703	21	17	350	350	NUM
ejpam-3703	21	18	347	347	NUM
ejpam-3703	21	19	proof	proof	NOUN
ejpam-3703	21	20	first	first	ADV
ejpam-3703	21	21	of	of	ADP
ejpam-3703	21	22	all	all	PRON
ejpam-3703	21	23	,	,	PUNCT
ejpam-3703	21	24	since	since	SCONJ
ejpam-3703	21	25	a	a	PRON
ejpam-3703	21	26	is	be	AUX
ejpam-3703	21	27	a	a	DET
ejpam-3703	21	28	right	right	ADJ
ejpam-3703	21	29	ideal	ideal	NOUN
ejpam-3703	21	30	and	and	CCONJ
ejpam-3703	21	31	b	b	NOUN
ejpam-3703	21	32	is	be	AUX
ejpam-3703	21	33	a	a	DET
ejpam-3703	21	34	left	left	ADJ
ejpam-3703	21	35	ideal	ideal	NOUN
ejpam-3703	21	36	of	of	ADP
ejpam-3703	21	37	s	s	PROPN
ejpam-3703	21	38	,	,	PUNCT
ejpam-3703	21	39	the	the	DET
ejpam-3703	21	40	intersection	intersection	NOUN
ejpam-3703	21	41	a	a	DET
ejpam-3703	21	42	∩	∩	ADJ
ejpam-3703	21	43	b	b	NOUN
ejpam-3703	21	44	is	be	AUX
ejpam-3703	21	45	nonempty	nonempty	ADJ
ejpam-3703	21	46	.	.	PUNCT
ejpam-3703	22	1	indeed	indeed	ADV
ejpam-3703	22	2	:	:	PUNCT
ejpam-3703	22	3	take	take	VERB
ejpam-3703	22	4	an	an	DET
ejpam-3703	22	5	element	element	NOUN
ejpam-3703	22	6	a	a	DET
ejpam-3703	22	7	∈	∈	PROPN
ejpam-3703	22	8	a	a	PRON
ejpam-3703	22	9	and	and	CCONJ
ejpam-3703	22	10	an	an	DET
ejpam-3703	22	11	element	element	NOUN
ejpam-3703	22	12	b	b	PROPN
ejpam-3703	22	13	∈	∈	PROPN
ejpam-3703	22	14	b	b	PROPN
ejpam-3703	22	15	(	(	PUNCT
ejpam-3703	22	16	a	a	PRON
ejpam-3703	22	17	,	,	PUNCT
ejpam-3703	22	18	b	b	NOUN
ejpam-3703	22	19	6=	6=	NUM
ejpam-3703	22	20	∅	∅	NOUN
ejpam-3703	22	21	)	)	PUNCT
ejpam-3703	22	22	;	;	PUNCT
ejpam-3703	22	23	then	then	ADV
ejpam-3703	22	24	a	a	DET
ejpam-3703	22	25	◦	◦	NOUN
ejpam-3703	22	26	b	b	NOUN
ejpam-3703	22	27	⊆	⊆	NUM
ejpam-3703	22	28	a	a	DET
ejpam-3703	22	29	∗	∗	NOUN
ejpam-3703	22	30	b	b	NOUN
ejpam-3703	22	31	⊆	⊆	NUM
ejpam-3703	22	32	a	a	DET
ejpam-3703	22	33	∗	∗	NOUN
ejpam-3703	22	34	s	s	NOUN
ejpam-3703	22	35	⊆	⊆	NUM
ejpam-3703	22	36	a	a	PRON
ejpam-3703	22	37	and	and	CCONJ
ejpam-3703	22	38	a	a	DET
ejpam-3703	22	39	◦	◦	NOUN
ejpam-3703	22	40	b	b	NUM
ejpam-3703	22	41	⊆	⊆	NUM
ejpam-3703	22	42	a	a	DET
ejpam-3703	22	43	∗	∗	NOUN
ejpam-3703	22	44	b	b	NOUN
ejpam-3703	23	1	⊆	⊆	NUM
ejpam-3703	23	2	s	s	NOUN
ejpam-3703	23	3	∗	∗	NOUN
ejpam-3703	23	4	b	b	NOUN
ejpam-3703	23	5	⊆	⊆	NUM
ejpam-3703	23	6	b	b	NOUN
ejpam-3703	23	7	,	,	PUNCT
ejpam-3703	23	8	so	so	SCONJ
ejpam-3703	23	9	a	a	DET
ejpam-3703	23	10	◦	◦	NOUN
ejpam-3703	23	11	b	b	NOUN
ejpam-3703	23	12	⊆	⊆	NUM
ejpam-3703	23	13	a	a	DET
ejpam-3703	23	14	∩	∩	ADJ
ejpam-3703	23	15	b.	b.	NOUN
ejpam-3703	23	16	since	since	SCONJ
ejpam-3703	23	17	a	a	DET
ejpam-3703	23	18	◦	◦	NOUN
ejpam-3703	23	19	b	b	NOUN
ejpam-3703	23	20	is	be	AUX
ejpam-3703	23	21	a	a	DET
ejpam-3703	23	22	nonempty	nonempty	ADJ
ejpam-3703	23	23	set	set	NOUN
ejpam-3703	23	24	,	,	PUNCT
ejpam-3703	23	25	the	the	DET
ejpam-3703	23	26	set	set	NOUN
ejpam-3703	23	27	a	a	DET
ejpam-3703	23	28	∩b	∩b	NOUN
ejpam-3703	23	29	is	be	AUX
ejpam-3703	23	30	nonempty	nonempty	ADJ
ejpam-3703	23	31	as	as	ADV
ejpam-3703	23	32	well	well	ADV
ejpam-3703	23	33	(	(	PUNCT
ejpam-3703	23	34	see	see	VERB
ejpam-3703	23	35	also	also	ADV
ejpam-3703	23	36	[	[	X
ejpam-3703	23	37	5	5	NUM
ejpam-3703	23	38	]	]	PUNCT
ejpam-3703	23	39	)	)	PUNCT
ejpam-3703	23	40	.	.	PUNCT
ejpam-3703	24	1	we	we	PRON
ejpam-3703	24	2	also	also	ADV
ejpam-3703	24	3	have	have	VERB
ejpam-3703	24	4	(	(	PUNCT
ejpam-3703	24	5	(	(	PUNCT
ejpam-3703	24	6	a	a	DET
ejpam-3703	24	7	∩b	∩b	NOUN
ejpam-3703	24	8	)	)	PUNCT
ejpam-3703	24	9	∗	∗	NOUN
ejpam-3703	24	10	s	s	PART
ejpam-3703	24	11	)	)	PUNCT
ejpam-3703	24	12	∩	∩	NOUN
ejpam-3703	24	13	(	(	PUNCT
ejpam-3703	24	14	s	s	X
ejpam-3703	24	15	∗	∗	NOUN
ejpam-3703	24	16	(	(	PUNCT
ejpam-3703	24	17	a	a	DET
ejpam-3703	24	18	∩b	∩b	NOUN
ejpam-3703	24	19	)	)	PUNCT
ejpam-3703	24	20	)	)	PUNCT
ejpam-3703	25	1	⊆	⊆	X
ejpam-3703	25	2	(	(	PUNCT
ejpam-3703	25	3	a	a	DET
ejpam-3703	25	4	∗	∗	NOUN
ejpam-3703	25	5	s	s	NOUN
ejpam-3703	25	6	)	)	PUNCT
ejpam-3703	25	7	∩	∩	NOUN
ejpam-3703	25	8	(	(	PUNCT
ejpam-3703	25	9	s	s	NOUN
ejpam-3703	25	10	∗b	∗b	PROPN
ejpam-3703	25	11	)	)	PUNCT
ejpam-3703	25	12	⊆	⊆	NUM
ejpam-3703	25	13	a	a	DET
ejpam-3703	25	14	∩b	∩b	NOUN
ejpam-3703	25	15	,	,	PUNCT
ejpam-3703	25	16	thus	thus	ADV
ejpam-3703	25	17	a	a	DET
ejpam-3703	25	18	∩b	∩b	NOUN
ejpam-3703	25	19	is	be	AUX
ejpam-3703	25	20	a	a	DET
ejpam-3703	25	21	quasi	quasi	NOUN
ejpam-3703	25	22	-	-	NOUN
ejpam-3703	25	23	ideal	ideal	NOUN
ejpam-3703	25	24	of	of	ADP
ejpam-3703	25	25	s.	s.	PROPN
ejpam-3703	25	26	�	�	PROPN
ejpam-3703	25	27	lemma	lemma	PROPN
ejpam-3703	25	28	4	4	NUM
ejpam-3703	25	29	[	[	SYM
ejpam-3703	25	30	4	4	NUM
ejpam-3703	25	31	,	,	PUNCT
ejpam-3703	25	32	5	5	NUM
ejpam-3703	25	33	]	]	PUNCT
ejpam-3703	25	34	an	an	DET
ejpam-3703	25	35	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	25	36	(	(	PUNCT
ejpam-3703	25	37	s	s	NOUN
ejpam-3703	25	38	,	,	PUNCT
ejpam-3703	25	39	◦	◦	NOUN
ejpam-3703	25	40	)	)	PUNCT
ejpam-3703	25	41	is	be	AUX
ejpam-3703	25	42	regular	regular	ADJ
ejpam-3703	25	43	if	if	SCONJ
ejpam-3703	25	44	and	and	CCONJ
ejpam-3703	25	45	only	only	ADV
ejpam-3703	25	46	if	if	SCONJ
ejpam-3703	25	47	,	,	PUNCT
ejpam-3703	25	48	for	for	ADP
ejpam-3703	25	49	every	every	DET
ejpam-3703	25	50	right	right	ADJ
ejpam-3703	25	51	ideal	ideal	NOUN
ejpam-3703	25	52	a	a	PRON
ejpam-3703	25	53	and	and	CCONJ
ejpam-3703	25	54	every	every	PRON
ejpam-3703	25	55	left	leave	VERB
ejpam-3703	25	56	ideal	ideal	PROPN
ejpam-3703	25	57	b	b	PROPN
ejpam-3703	25	58	of	of	ADP
ejpam-3703	25	59	s	s	PROPN
ejpam-3703	25	60	,	,	PUNCT
ejpam-3703	25	61	we	we	PRON
ejpam-3703	25	62	have	have	VERB
ejpam-3703	25	63	a	a	DET
ejpam-3703	25	64	∩b	∩b	NOUN
ejpam-3703	25	65	⊆	⊆	NUM
ejpam-3703	25	66	a	a	DET
ejpam-3703	25	67	∗b	∗b	PROPN
ejpam-3703	25	68	(	(	PUNCT
ejpam-3703	25	69	equivalently	equivalently	ADV
ejpam-3703	25	70	,	,	PUNCT
ejpam-3703	25	71	a	a	DET
ejpam-3703	25	72	∩b	∩b	NOUN
ejpam-3703	25	73	=	=	PUNCT
ejpam-3703	25	74	a	a	DET
ejpam-3703	25	75	∗b	∗b	NOUN
ejpam-3703	25	76	)	)	PUNCT
ejpam-3703	25	77	.	.	PUNCT
ejpam-3703	26	1	lemma	lemma	PROPN
ejpam-3703	26	2	5	5	NUM
ejpam-3703	26	3	if	if	SCONJ
ejpam-3703	26	4	(	(	PUNCT
ejpam-3703	26	5	s	s	NOUN
ejpam-3703	26	6	,	,	PUNCT
ejpam-3703	26	7	◦	◦	NOUN
ejpam-3703	26	8	)	)	PUNCT
ejpam-3703	26	9	is	be	AUX
ejpam-3703	26	10	a	a	DET
ejpam-3703	26	11	regular	regular	ADJ
ejpam-3703	26	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	26	13	,	,	PUNCT
ejpam-3703	26	14	then	then	ADV
ejpam-3703	26	15	s	s	VERB
ejpam-3703	26	16	∗	∗	NOUN
ejpam-3703	26	17	s	s	PART
ejpam-3703	26	18	=	=	PUNCT
ejpam-3703	26	19	s.	s.	PROPN
ejpam-3703	26	20	proof	proof	NOUN
ejpam-3703	26	21	since	since	SCONJ
ejpam-3703	26	22	s	s	PROPN
ejpam-3703	26	23	is	be	AUX
ejpam-3703	26	24	regular	regular	ADJ
ejpam-3703	26	25	,	,	PUNCT
ejpam-3703	26	26	for	for	SCONJ
ejpam-3703	26	27	every	every	DET
ejpam-3703	26	28	nonempty	nonempty	NOUN
ejpam-3703	26	29	subset	subset	VERB
ejpam-3703	26	30	a	a	PRON
ejpam-3703	26	31	of	of	ADP
ejpam-3703	26	32	s	s	PROPN
ejpam-3703	26	33	,	,	PUNCT
ejpam-3703	26	34	by	by	ADP
ejpam-3703	26	35	lemma	lemma	PROPN
ejpam-3703	26	36	2	2	NUM
ejpam-3703	26	37	,	,	PUNCT
ejpam-3703	26	38	we	we	PRON
ejpam-3703	26	39	have	have	VERB
ejpam-3703	26	40	a	a	DET
ejpam-3703	26	41	⊆	⊆	NUM
ejpam-3703	26	42	a	a	DET
ejpam-3703	26	43	∗	∗	NOUN
ejpam-3703	26	44	s	s	NOUN
ejpam-3703	26	45	∗a	∗a	ADJ
ejpam-3703	26	46	.	.	PUNCT
ejpam-3703	27	1	thus	thus	ADV
ejpam-3703	27	2	we	we	PRON
ejpam-3703	27	3	have	have	VERB
ejpam-3703	27	4	s	s	VERB
ejpam-3703	27	5	⊆	⊆	NUM
ejpam-3703	27	6	(	(	PUNCT
ejpam-3703	27	7	s	s	NOUN
ejpam-3703	27	8	∗	∗	PRON
ejpam-3703	27	9	s	s	NOUN
ejpam-3703	27	10	)	)	PUNCT
ejpam-3703	27	11	∗	∗	NOUN
ejpam-3703	27	12	s	s	NOUN
ejpam-3703	27	13	⊆	⊆	NUM
ejpam-3703	27	14	s	s	NOUN
ejpam-3703	27	15	∗	∗	NOUN
ejpam-3703	27	16	s	s	NOUN
ejpam-3703	27	17	⊆	⊆	NUM
ejpam-3703	27	18	s	s	NOUN
ejpam-3703	27	19	and	and	CCONJ
ejpam-3703	27	20	so	so	ADV
ejpam-3703	27	21	s	s	VERB
ejpam-3703	27	22	∗	∗	NOUN
ejpam-3703	27	23	s	s	PART
ejpam-3703	27	24	=	=	PUNCT
ejpam-3703	27	25	s.	s.	PROPN
ejpam-3703	27	26	�	�	PROPN
ejpam-3703	27	27	a	a	PRON
ejpam-3703	27	28	semigroup	semigroup	NOUN
ejpam-3703	27	29	(	(	PUNCT
ejpam-3703	27	30	s	s	PROPN
ejpam-3703	27	31	,	,	PUNCT
ejpam-3703	27	32	·	·	PUNCT
ejpam-3703	27	33	)	)	PUNCT
ejpam-3703	27	34	is	be	AUX
ejpam-3703	27	35	called	call	VERB
ejpam-3703	27	36	von	von	PROPN
ejpam-3703	27	37	neumann	neumann	PROPN
ejpam-3703	27	38	regular	regular	PROPN
ejpam-3703	27	39	(	(	PUNCT
ejpam-3703	27	40	or	or	CCONJ
ejpam-3703	27	41	just	just	ADV
ejpam-3703	27	42	regular	regular	ADJ
ejpam-3703	27	43	)	)	PUNCT
ejpam-3703	27	44	if	if	SCONJ
ejpam-3703	27	45	for	for	ADP
ejpam-3703	27	46	each	each	DET
ejpam-3703	27	47	a	a	DET
ejpam-3703	27	48	∈	∈	NOUN
ejpam-3703	27	49	s	s	VERB
ejpam-3703	27	50	there	there	PRON
ejpam-3703	27	51	exists	exist	VERB
ejpam-3703	27	52	x	x	X
ejpam-3703	27	53	∈	∈	NOUN
ejpam-3703	27	54	s	s	VERB
ejpam-3703	27	55	such	such	ADJ
ejpam-3703	27	56	that	that	SCONJ
ejpam-3703	27	57	a	a	DET
ejpam-3703	27	58	=	=	X
ejpam-3703	27	59	axa	axa	NOUN
ejpam-3703	28	1	[	[	X
ejpam-3703	28	2	1	1	NUM
ejpam-3703	28	3	,	,	PUNCT
ejpam-3703	28	4	8	8	NUM
ejpam-3703	28	5	]	]	PUNCT
ejpam-3703	28	6	.	.	PUNCT
ejpam-3703	29	1	as	as	SCONJ
ejpam-3703	29	2	always	always	ADV
ejpam-3703	29	3	,	,	PUNCT
ejpam-3703	29	4	p∗(s	p∗(s	NOUN
ejpam-3703	29	5	)	)	PUNCT
ejpam-3703	29	6	denotes	denote	VERB
ejpam-3703	29	7	the	the	DET
ejpam-3703	29	8	set	set	NOUN
ejpam-3703	29	9	of	of	ADP
ejpam-3703	29	10	all	all	DET
ejpam-3703	29	11	nonempty	nonempty	ADJ
ejpam-3703	29	12	subsets	subset	NOUN
ejpam-3703	29	13	of	of	ADP
ejpam-3703	29	14	s.	s.	PROPN
ejpam-3703	29	15	theorem	theorem	VERB
ejpam-3703	29	16	6	6	NUM
ejpam-3703	29	17	an	an	DET
ejpam-3703	29	18	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	29	19	(	(	PUNCT
ejpam-3703	29	20	s	s	NOUN
ejpam-3703	29	21	,	,	PUNCT
ejpam-3703	29	22	◦	◦	NOUN
ejpam-3703	29	23	)	)	PUNCT
ejpam-3703	29	24	is	be	AUX
ejpam-3703	29	25	regular	regular	ADJ
ejpam-3703	29	26	if	if	SCONJ
ejpam-3703	30	1	and	and	CCONJ
ejpam-3703	30	2	only	only	ADV
ejpam-3703	30	3	if	if	SCONJ
ejpam-3703	30	4	the	the	DET
ejpam-3703	30	5	set	set	NOUN
ejpam-3703	30	6	q	q	NOUN
ejpam-3703	30	7	of	of	ADP
ejpam-3703	30	8	all	all	DET
ejpam-3703	30	9	quasi	quasi	NOUN
ejpam-3703	30	10	-	-	NOUN
ejpam-3703	30	11	ideals	ideal	NOUN
ejpam-3703	30	12	of	of	ADP
ejpam-3703	30	13	s	s	NOUN
ejpam-3703	30	14	with	with	ADP
ejpam-3703	30	15	the	the	DET
ejpam-3703	30	16	multiplication	multiplication	NOUN
ejpam-3703	30	17	“	"	PUNCT
ejpam-3703	30	18	∗	∗	NOUN
ejpam-3703	30	19	”	"	PUNCT
ejpam-3703	30	20	of	of	ADP
ejpam-3703	30	21	p∗(s	p∗(s	NOUN
ejpam-3703	30	22	)	)	PUNCT
ejpam-3703	30	23	is	be	AUX
ejpam-3703	30	24	a	a	DET
ejpam-3703	30	25	von	von	PROPN
ejpam-3703	30	26	neumann	neumann	PROPN
ejpam-3703	30	27	regular	regular	PROPN
ejpam-3703	30	28	semigroup	semigroup	PROPN
ejpam-3703	30	29	.	.	PUNCT
ejpam-3703	31	1	proof	proof	NOUN
ejpam-3703	31	2	=	=	PRON
ejpam-3703	31	3	⇒.	⇒.	PROPN
ejpam-3703	31	4	first	first	ADV
ejpam-3703	31	5	of	of	ADP
ejpam-3703	31	6	all	all	PRON
ejpam-3703	31	7	,	,	PUNCT
ejpam-3703	31	8	for	for	ADP
ejpam-3703	31	9	every	every	DET
ejpam-3703	31	10	quasi	quasi	ADJ
ejpam-3703	31	11	-	-	ADJ
ejpam-3703	31	12	ideal	ideal	ADJ
ejpam-3703	31	13	q	q	NOUN
ejpam-3703	31	14	of	of	ADP
ejpam-3703	31	15	s	s	PROPN
ejpam-3703	31	16	,	,	PUNCT
ejpam-3703	31	17	we	we	PRON
ejpam-3703	31	18	have	have	VERB
ejpam-3703	31	19	q	q	NOUN
ejpam-3703	31	20	=	=	PUNCT
ejpam-3703	31	21	(	(	PUNCT
ejpam-3703	31	22	q	q	NOUN
ejpam-3703	31	23	∗	∗	NUM
ejpam-3703	31	24	s	s	NOUN
ejpam-3703	31	25	)	)	PUNCT
ejpam-3703	31	26	∩	∩	NOUN
ejpam-3703	31	27	(	(	PUNCT
ejpam-3703	31	28	s	s	X
ejpam-3703	31	29	∗q	∗q	PROPN
ejpam-3703	31	30	)	)	PUNCT
ejpam-3703	31	31	(	(	PUNCT
ejpam-3703	31	32	1	1	X
ejpam-3703	31	33	)	)	PUNCT
ejpam-3703	31	34	in	in	ADP
ejpam-3703	31	35	fact	fact	NOUN
ejpam-3703	31	36	:	:	PUNCT
ejpam-3703	31	37	since	since	SCONJ
ejpam-3703	31	38	s	s	NOUN
ejpam-3703	31	39	is	be	AUX
ejpam-3703	31	40	regular	regular	ADJ
ejpam-3703	31	41	,	,	PUNCT
ejpam-3703	31	42	r(q	r(q	PROPN
ejpam-3703	31	43	)	)	PUNCT
ejpam-3703	31	44	is	be	AUX
ejpam-3703	31	45	a	a	DET
ejpam-3703	31	46	right	right	ADJ
ejpam-3703	31	47	ideal	ideal	NOUN
ejpam-3703	31	48	and	and	CCONJ
ejpam-3703	31	49	l(q	l(q	PROPN
ejpam-3703	31	50	)	)	PUNCT
ejpam-3703	31	51	is	be	AUX
ejpam-3703	31	52	a	a	DET
ejpam-3703	31	53	left	left	ADJ
ejpam-3703	31	54	ideal	ideal	NOUN
ejpam-3703	31	55	of	of	ADP
ejpam-3703	31	56	(	(	PUNCT
ejpam-3703	31	57	s	s	NOUN
ejpam-3703	31	58	,	,	PUNCT
ejpam-3703	31	59	◦	◦	NOUN
ejpam-3703	31	60	)	)	PUNCT
ejpam-3703	31	61	,	,	PUNCT
ejpam-3703	31	62	by	by	ADP
ejpam-3703	31	63	lemma	lemma	PROPN
ejpam-3703	31	64	1	1	NUM
ejpam-3703	31	65	,	,	PUNCT
ejpam-3703	31	66	they	they	PRON
ejpam-3703	31	67	are	be	AUX
ejpam-3703	31	68	idempotent	idempotent	ADJ
ejpam-3703	31	69	and	and	CCONJ
ejpam-3703	31	70	we	we	PRON
ejpam-3703	31	71	have	have	VERB
ejpam-3703	31	72	q	q	NOUN
ejpam-3703	31	73	⊆	⊆	NUM
ejpam-3703	31	74	q	q	NOUN
ejpam-3703	31	75	∪	∪	ADJ
ejpam-3703	31	76	(	(	PUNCT
ejpam-3703	31	77	q	q	NOUN
ejpam-3703	31	78	∗	∗	NUM
ejpam-3703	31	79	s	s	PART
ejpam-3703	31	80	)	)	PUNCT
ejpam-3703	31	81	=	=	SYM
ejpam-3703	31	82	r(q	r(q	PROPN
ejpam-3703	31	83	)	)	PUNCT
ejpam-3703	31	84	=	=	SYM
ejpam-3703	31	85	r(q	r(q	PROPN
ejpam-3703	31	86	)	)	PUNCT
ejpam-3703	31	87	∗r(q	∗r(q	NOUN
ejpam-3703	31	88	)	)	PUNCT
ejpam-3703	31	89	=	=	PRON
ejpam-3703	32	1	(	(	PUNCT
ejpam-3703	32	2	q	q	NOUN
ejpam-3703	32	3	∪	∪	X
ejpam-3703	32	4	(	(	PUNCT
ejpam-3703	32	5	q	q	NOUN
ejpam-3703	32	6	∗	∗	NOUN
ejpam-3703	32	7	s	s	NOUN
ejpam-3703	32	8	)	)	PUNCT
ejpam-3703	32	9	)	)	PUNCT
ejpam-3703	32	10	∗	∗	NOUN
ejpam-3703	32	11	(	(	PUNCT
ejpam-3703	32	12	q	q	NOUN
ejpam-3703	32	13	∪	∪	X
ejpam-3703	32	14	(	(	PUNCT
ejpam-3703	32	15	q	q	NOUN
ejpam-3703	32	16	∗	∗	NOUN
ejpam-3703	32	17	s	s	NOUN
ejpam-3703	32	18	)	)	PUNCT
ejpam-3703	32	19	)	)	PUNCT
ejpam-3703	33	1	=	=	PUNCT
ejpam-3703	33	2	q	q	PROPN
ejpam-3703	33	3	∗q	∗q	PROPN
ejpam-3703	33	4	∪q	∪q	NUM
ejpam-3703	33	5	∗	∗	NOUN
ejpam-3703	33	6	s	s	PART
ejpam-3703	33	7	∗q	∗q	PROPN
ejpam-3703	33	8	∪q	∪q	NUM
ejpam-3703	33	9	∗q	∗q	PROPN
ejpam-3703	33	10	∗	∗	NOUN
ejpam-3703	33	11	s	s	PART
ejpam-3703	33	12	∪q	∪q	X
ejpam-3703	33	13	∗	∗	NOUN
ejpam-3703	33	14	s	s	PART
ejpam-3703	33	15	∗q	∗q	PROPN
ejpam-3703	33	16	∗	∗	NOUN
ejpam-3703	33	17	s	s	NOUN
ejpam-3703	33	18	⊆	⊆	NUM
ejpam-3703	33	19	q	q	NOUN
ejpam-3703	33	20	∗	∗	PRON
ejpam-3703	33	21	s	s	NOUN
ejpam-3703	33	22	and	and	CCONJ
ejpam-3703	33	23	q	q	NOUN
ejpam-3703	34	1	⊆	⊆	NUM
ejpam-3703	34	2	q	q	NOUN
ejpam-3703	34	3	∪	∪	ADJ
ejpam-3703	34	4	(	(	PUNCT
ejpam-3703	34	5	s	s	X
ejpam-3703	34	6	∗q	∗q	PROPN
ejpam-3703	34	7	)	)	PUNCT
ejpam-3703	34	8	=	=	SYM
ejpam-3703	34	9	l(q	l(q	PROPN
ejpam-3703	34	10	)	)	PUNCT
ejpam-3703	34	11	=	=	SYM
ejpam-3703	34	12	l(q	l(q	PROPN
ejpam-3703	34	13	)	)	PUNCT
ejpam-3703	34	14	∗	∗	NOUN
ejpam-3703	34	15	l(q	l(q	PROPN
ejpam-3703	34	16	)	)	PUNCT
ejpam-3703	35	1	=	=	PRON
ejpam-3703	35	2	(	(	PUNCT
ejpam-3703	35	3	q	q	NOUN
ejpam-3703	35	4	∪	∪	X
ejpam-3703	35	5	(	(	PUNCT
ejpam-3703	35	6	s	s	X
ejpam-3703	35	7	∗q	∗q	PROPN
ejpam-3703	35	8	)	)	PUNCT
ejpam-3703	35	9	)	)	PUNCT
ejpam-3703	35	10	∗	∗	NOUN
ejpam-3703	35	11	(	(	PUNCT
ejpam-3703	35	12	q	q	NOUN
ejpam-3703	35	13	∪	∪	X
ejpam-3703	35	14	(	(	PUNCT
ejpam-3703	35	15	s	s	X
ejpam-3703	35	16	∗q	∗q	PROPN
ejpam-3703	35	17	)	)	PUNCT
ejpam-3703	35	18	)	)	PUNCT
ejpam-3703	36	1	=	=	PUNCT
ejpam-3703	36	2	q	q	PROPN
ejpam-3703	36	3	∗q	∗q	PROPN
ejpam-3703	36	4	∪	∪	ADP
ejpam-3703	36	5	s	s	PART
ejpam-3703	36	6	∗q	∗q	PROPN
ejpam-3703	36	7	∗q	∗q	PROPN
ejpam-3703	36	8	∪q	∪q	X
ejpam-3703	36	9	∗	∗	NOUN
ejpam-3703	36	10	s	s	PART
ejpam-3703	36	11	∗q	∗q	PROPN
ejpam-3703	36	12	∪	∪	PROPN
ejpam-3703	36	13	s	s	PART
ejpam-3703	36	14	∗q	∗q	PROPN
ejpam-3703	36	15	∗	∗	NOUN
ejpam-3703	36	16	s	s	PART
ejpam-3703	36	17	∗q	∗q	PROPN
ejpam-3703	36	18	⊆	⊆	NUM
ejpam-3703	36	19	s	s	PART
ejpam-3703	36	20	∗q	∗q	PROPN
ejpam-3703	36	21	.	.	PUNCT
ejpam-3703	37	1	thus	thus	ADV
ejpam-3703	37	2	we	we	PRON
ejpam-3703	37	3	have	have	VERB
ejpam-3703	37	4	q	q	NOUN
ejpam-3703	37	5	⊆	⊆	NUM
ejpam-3703	37	6	(	(	PUNCT
ejpam-3703	37	7	q	q	NOUN
ejpam-3703	37	8	∗	∗	NUM
ejpam-3703	37	9	s	s	NOUN
ejpam-3703	37	10	)	)	PUNCT
ejpam-3703	37	11	∩	∩	NOUN
ejpam-3703	37	12	(	(	PUNCT
ejpam-3703	37	13	s	s	PROPN
ejpam-3703	37	14	∗q	∗q	NOUN
ejpam-3703	37	15	)	)	PUNCT
ejpam-3703	37	16	⊆	⊆	NUM
ejpam-3703	37	17	q	q	NOUN
ejpam-3703	37	18	,	,	PUNCT
ejpam-3703	37	19	then	then	ADV
ejpam-3703	37	20	q	q	NOUN
ejpam-3703	37	21	=	=	PUNCT
ejpam-3703	37	22	(	(	PUNCT
ejpam-3703	37	23	q	q	NOUN
ejpam-3703	37	24	∗	∗	NUM
ejpam-3703	37	25	s	s	NOUN
ejpam-3703	37	26	)	)	PUNCT
ejpam-3703	37	27	∩	∩	NOUN
ejpam-3703	37	28	(	(	PUNCT
ejpam-3703	37	29	s	s	PROPN
ejpam-3703	37	30	∗q	∗q	PROPN
ejpam-3703	37	31	)	)	PUNCT
ejpam-3703	37	32	and	and	CCONJ
ejpam-3703	37	33	property	property	NOUN
ejpam-3703	37	34	(	(	PUNCT
ejpam-3703	37	35	1	1	NUM
ejpam-3703	37	36	)	)	PUNCT
ejpam-3703	37	37	is	be	AUX
ejpam-3703	37	38	satisfied	satisfied	ADJ
ejpam-3703	37	39	.	.	PUNCT
ejpam-3703	38	1	in	in	ADP
ejpam-3703	38	2	addition	addition	NOUN
ejpam-3703	38	3	,	,	PUNCT
ejpam-3703	38	4	since	since	SCONJ
ejpam-3703	38	5	s	s	NOUN
ejpam-3703	38	6	is	be	AUX
ejpam-3703	38	7	regular	regular	ADJ
ejpam-3703	38	8	,	,	PUNCT
ejpam-3703	38	9	a	a	PRON
ejpam-3703	38	10	is	be	AUX
ejpam-3703	38	11	a	a	DET
ejpam-3703	38	12	right	right	ADJ
ejpam-3703	38	13	ideal	ideal	NOUN
ejpam-3703	38	14	and	and	CCONJ
ejpam-3703	38	15	b	b	NOUN
ejpam-3703	38	16	is	be	AUX
ejpam-3703	38	17	a	a	DET
ejpam-3703	38	18	left	left	ADJ
ejpam-3703	38	19	ideal	ideal	NOUN
ejpam-3703	38	20	of	of	ADP
ejpam-3703	38	21	s	s	PROPN
ejpam-3703	38	22	,	,	PUNCT
ejpam-3703	38	23	by	by	ADP
ejpam-3703	38	24	lemmas	lemmas	PROPN
ejpam-3703	38	25	3	3	NUM
ejpam-3703	38	26	and	and	CCONJ
ejpam-3703	38	27	4	4	NUM
ejpam-3703	38	28	,	,	PUNCT
ejpam-3703	38	29	a	a	DET
ejpam-3703	38	30	∗b	∗b	PROPN
ejpam-3703	38	31	is	be	AUX
ejpam-3703	38	32	a	a	DET
ejpam-3703	38	33	quasi	quasi	NOUN
ejpam-3703	38	34	-	-	NOUN
ejpam-3703	38	35	ideal	ideal	NOUN
ejpam-3703	38	36	of	of	ADP
ejpam-3703	38	37	s.	s.	PROPN
ejpam-3703	38	38	so	so	ADV
ejpam-3703	38	39	,	,	PUNCT
ejpam-3703	38	40	by	by	ADP
ejpam-3703	38	41	(	(	PUNCT
ejpam-3703	38	42	1	1	NUM
ejpam-3703	38	43	)	)	PUNCT
ejpam-3703	38	44	,	,	PUNCT
ejpam-3703	38	45	we	we	PRON
ejpam-3703	38	46	have	have	VERB
ejpam-3703	38	47	a	a	DET
ejpam-3703	38	48	∗b	∗b	NOUN
ejpam-3703	38	49	=	=	SYM
ejpam-3703	38	50	(	(	PUNCT
ejpam-3703	38	51	a	a	DET
ejpam-3703	38	52	∗b	∗b	PROPN
ejpam-3703	38	53	∗	∗	NOUN
ejpam-3703	38	54	s	s	NOUN
ejpam-3703	38	55	)	)	PUNCT
ejpam-3703	38	56	∩	∩	NOUN
ejpam-3703	38	57	(	(	PUNCT
ejpam-3703	38	58	s	s	PROPN
ejpam-3703	38	59	∗a	∗a	PROPN
ejpam-3703	38	60	∗b	∗b	PROPN
ejpam-3703	38	61	)	)	PUNCT
ejpam-3703	38	62	(	(	PUNCT
ejpam-3703	38	63	2	2	X
ejpam-3703	38	64	)	)	PUNCT
ejpam-3703	38	65	we	we	PRON
ejpam-3703	38	66	are	be	AUX
ejpam-3703	38	67	ready	ready	ADJ
ejpam-3703	38	68	now	now	ADV
ejpam-3703	38	69	to	to	PART
ejpam-3703	38	70	prove	prove	VERB
ejpam-3703	38	71	that	that	SCONJ
ejpam-3703	38	72	(	(	PUNCT
ejpam-3703	38	73	q	q	X
ejpam-3703	38	74	,	,	PUNCT
ejpam-3703	38	75	∗	∗	NOUN
ejpam-3703	38	76	)	)	PUNCT
ejpam-3703	38	77	is	be	AUX
ejpam-3703	38	78	a	a	DET
ejpam-3703	38	79	von	von	PROPN
ejpam-3703	38	80	neumann	neumann	PROPN
ejpam-3703	38	81	regular	regular	PROPN
ejpam-3703	38	82	semigroup	semigroup	PROPN
ejpam-3703	38	83	.	.	PUNCT
ejpam-3703	39	1	in	in	ADP
ejpam-3703	39	2	this	this	DET
ejpam-3703	39	3	respect	respect	NOUN
ejpam-3703	39	4	,	,	PUNCT
ejpam-3703	39	5	we	we	PRON
ejpam-3703	39	6	prove	prove	VERB
ejpam-3703	39	7	the	the	DET
ejpam-3703	39	8	following	following	NOUN
ejpam-3703	39	9	:	:	PUNCT
ejpam-3703	39	10	n.	n.	PROPN
ejpam-3703	39	11	kehayopulu	kehayopulu	PROPN
ejpam-3703	39	12	/	/	SYM
ejpam-3703	39	13	eur	eur	PROPN
ejpam-3703	39	14	.	.	PUNCT
ejpam-3703	40	1	j.	j.	PROPN
ejpam-3703	40	2	pure	pure	PROPN
ejpam-3703	40	3	appl	appl	PROPN
ejpam-3703	40	4	.	.	PROPN
ejpam-3703	40	5	math	math	PROPN
ejpam-3703	40	6	,	,	PUNCT
ejpam-3703	40	7	13	13	NUM
ejpam-3703	40	8	(	(	PUNCT
ejpam-3703	40	9	2	2	NUM
ejpam-3703	40	10	)	)	PUNCT
ejpam-3703	40	11	(	(	PUNCT
ejpam-3703	40	12	2020	2020	NUM
ejpam-3703	40	13	)	)	PUNCT
ejpam-3703	40	14	,	,	PUNCT
ejpam-3703	40	15	346	346	NUM
ejpam-3703	40	16	-	-	SYM
ejpam-3703	40	17	350	350	NUM
ejpam-3703	40	18	348	348	NUM
ejpam-3703	40	19	(	(	PUNCT
ejpam-3703	40	20	q	q	NOUN
ejpam-3703	40	21	,	,	PUNCT
ejpam-3703	40	22	∗	∗	NOUN
ejpam-3703	40	23	)	)	PUNCT
ejpam-3703	40	24	is	be	AUX
ejpam-3703	40	25	semigroup	semigroup	PROPN
ejpam-3703	40	26	.	.	PUNCT
ejpam-3703	41	1	indeed	indeed	ADV
ejpam-3703	41	2	:	:	PUNCT
ejpam-3703	41	3	first	first	ADV
ejpam-3703	41	4	of	of	ADP
ejpam-3703	41	5	all	all	PRON
ejpam-3703	41	6	,	,	PUNCT
ejpam-3703	41	7	in	in	ADP
ejpam-3703	41	8	an	an	DET
ejpam-3703	41	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	41	10	,	,	PUNCT
ejpam-3703	41	11	the	the	DET
ejpam-3703	41	12	operation	operation	NOUN
ejpam-3703	41	13	“	"	PUNCT
ejpam-3703	41	14	∗	∗	NOUN
ejpam-3703	41	15	”	"	PUNCT
ejpam-3703	41	16	is	be	AUX
ejpam-3703	41	17	associative	associative	ADJ
ejpam-3703	41	18	(	(	PUNCT
ejpam-3703	41	19	see	see	VERB
ejpam-3703	41	20	[	[	X
ejpam-3703	41	21	5	5	NUM
ejpam-3703	41	22	]	]	PUNCT
ejpam-3703	41	23	,	,	PUNCT
ejpam-3703	41	24	also	also	ADV
ejpam-3703	41	25	[	[	X
ejpam-3703	41	26	6	6	NUM
ejpam-3703	41	27	;	;	PUNCT
ejpam-3703	41	28	p.	p.	NOUN
ejpam-3703	41	29	22	22	NUM
ejpam-3703	41	30	]	]	PUNCT
ejpam-3703	41	31	)	)	PUNCT
ejpam-3703	41	32	.	.	PUNCT
ejpam-3703	42	1	let	let	VERB
ejpam-3703	42	2	now	now	ADV
ejpam-3703	42	3	q1	q1	VERB
ejpam-3703	42	4	,	,	PUNCT
ejpam-3703	42	5	q2	q2	NOUN
ejpam-3703	42	6	be	be	VERB
ejpam-3703	42	7	quasi	quasi	NOUN
ejpam-3703	42	8	-	-	NOUN
ejpam-3703	42	9	ideals	ideal	NOUN
ejpam-3703	42	10	of	of	ADP
ejpam-3703	42	11	s.	s.	PROPN
ejpam-3703	42	12	then	then	ADV
ejpam-3703	42	13	q1	q1	PROPN
ejpam-3703	42	14	∗q2	∗q2	PROPN
ejpam-3703	42	15	is	be	AUX
ejpam-3703	42	16	a	a	DET
ejpam-3703	42	17	quasi	quasi	NOUN
ejpam-3703	42	18	-	-	NOUN
ejpam-3703	42	19	ideal	ideal	NOUN
ejpam-3703	42	20	of	of	ADP
ejpam-3703	42	21	s.	s.	PROPN
ejpam-3703	42	22	indeed	indeed	ADV
ejpam-3703	42	23	:	:	PUNCT
ejpam-3703	42	24	since	since	SCONJ
ejpam-3703	42	25	s	s	NOUN
ejpam-3703	42	26	is	be	AUX
ejpam-3703	42	27	regular	regular	ADJ
ejpam-3703	42	28	,	,	PUNCT
ejpam-3703	42	29	q1	q1	PROPN
ejpam-3703	42	30	∗q2	∗q2	ADJ
ejpam-3703	42	31	∗	∗	NOUN
ejpam-3703	42	32	s	s	PART
ejpam-3703	42	33	is	be	AUX
ejpam-3703	42	34	a	a	DET
ejpam-3703	42	35	right	right	ADJ
ejpam-3703	42	36	ideal	ideal	NOUN
ejpam-3703	42	37	and	and	CCONJ
ejpam-3703	42	38	s	s	PRON
ejpam-3703	42	39	∗q1	∗q1	X
ejpam-3703	42	40	∗q2	∗q2	ADJ
ejpam-3703	42	41	is	be	AUX
ejpam-3703	42	42	a	a	DET
ejpam-3703	42	43	left	left	ADJ
ejpam-3703	42	44	ideal	ideal	NOUN
ejpam-3703	42	45	of	of	ADP
ejpam-3703	42	46	s	s	PROPN
ejpam-3703	42	47	,	,	PUNCT
ejpam-3703	42	48	by	by	ADP
ejpam-3703	42	49	lemma	lemma	PROPN
ejpam-3703	42	50	1	1	NUM
ejpam-3703	42	51	,	,	PUNCT
ejpam-3703	42	52	they	they	PRON
ejpam-3703	42	53	are	be	AUX
ejpam-3703	42	54	idempotent	idempotent	ADJ
ejpam-3703	42	55	and	and	CCONJ
ejpam-3703	42	56	we	we	PRON
ejpam-3703	42	57	have	have	VERB
ejpam-3703	42	58	(	(	PUNCT
ejpam-3703	42	59	(	(	PUNCT
ejpam-3703	42	60	q1	q1	PROPN
ejpam-3703	42	61	∗q2	∗q2	ADJ
ejpam-3703	42	62	)	)	PUNCT
ejpam-3703	42	63	∗	∗	NOUN
ejpam-3703	42	64	s	s	PART
ejpam-3703	42	65	)	)	PUNCT
ejpam-3703	42	66	∩	∩	NOUN
ejpam-3703	42	67	(	(	PUNCT
ejpam-3703	42	68	s	s	NOUN
ejpam-3703	42	69	∗	∗	NOUN
ejpam-3703	42	70	(	(	PUNCT
ejpam-3703	42	71	q1	q1	PROPN
ejpam-3703	42	72	∗q2	∗q2	ADJ
ejpam-3703	42	73	)	)	PUNCT
ejpam-3703	42	74	)	)	PUNCT
ejpam-3703	43	1	=	=	SYM
ejpam-3703	43	2	(	(	PUNCT
ejpam-3703	43	3	q1	q1	PROPN
ejpam-3703	43	4	∗q2	∗q2	PROPN
ejpam-3703	43	5	∗	∗	NOUN
ejpam-3703	43	6	s	s	NOUN
ejpam-3703	43	7	)	)	PUNCT
ejpam-3703	43	8	∗	∗	NOUN
ejpam-3703	43	9	(	(	PUNCT
ejpam-3703	43	10	q1	q1	PROPN
ejpam-3703	43	11	∗q2	∗q2	ADJ
ejpam-3703	43	12	∗	∗	NOUN
ejpam-3703	43	13	s	s	NOUN
ejpam-3703	43	14	)	)	PUNCT
ejpam-3703	43	15	∩	∩	NOUN
ejpam-3703	43	16	(	(	PUNCT
ejpam-3703	43	17	s	s	PROPN
ejpam-3703	43	18	∗q1	∗q1	X
ejpam-3703	43	19	∗q2	∗q2	ADJ
ejpam-3703	43	20	)	)	PUNCT
ejpam-3703	43	21	∗	∗	NOUN
ejpam-3703	43	22	(	(	PUNCT
ejpam-3703	43	23	s	s	PROPN
ejpam-3703	43	24	∗q1	∗q1	X
ejpam-3703	43	25	∗q2	∗q2	ADJ
ejpam-3703	43	26	)	)	PUNCT
ejpam-3703	43	27	=	=	SYM
ejpam-3703	43	28	(	(	PUNCT
ejpam-3703	43	29	q1	q1	PROPN
ejpam-3703	43	30	∗q2	∗q2	ADJ
ejpam-3703	43	31	∗	∗	NOUN
ejpam-3703	43	32	s	s	PART
ejpam-3703	43	33	∗	∗	NOUN
ejpam-3703	43	34	s	s	NOUN
ejpam-3703	43	35	)	)	PUNCT
ejpam-3703	43	36	∗	∗	NOUN
ejpam-3703	43	37	(	(	PUNCT
ejpam-3703	43	38	q1	q1	PROPN
ejpam-3703	43	39	∗q2	∗q2	ADJ
ejpam-3703	43	40	∗	∗	NOUN
ejpam-3703	43	41	s	s	NOUN
ejpam-3703	43	42	)	)	PUNCT
ejpam-3703	43	43	∩	∩	NOUN
ejpam-3703	43	44	(	(	PUNCT
ejpam-3703	43	45	s	s	PROPN
ejpam-3703	43	46	∗q1	∗q1	X
ejpam-3703	43	47	∗q2	∗q2	ADJ
ejpam-3703	43	48	)	)	PUNCT
ejpam-3703	43	49	∗	∗	NOUN
ejpam-3703	43	50	(	(	PUNCT
ejpam-3703	43	51	s	s	NOUN
ejpam-3703	43	52	∗	∗	NOUN
ejpam-3703	43	53	s	s	X
ejpam-3703	43	54	∗q1	∗q1	X
ejpam-3703	43	55	∗q2	∗q2	ADJ
ejpam-3703	43	56	)	)	PUNCT
ejpam-3703	43	57	(	(	PUNCT
ejpam-3703	43	58	since	since	SCONJ
ejpam-3703	43	59	s	s	ADP
ejpam-3703	43	60	∗	∗	NOUN
ejpam-3703	43	61	s	s	PART
ejpam-3703	43	62	=	=	SYM
ejpam-3703	43	63	s	s	NOUN
ejpam-3703	43	64	)	)	PUNCT
ejpam-3703	43	65	=	=	SYM
ejpam-3703	43	66	(	(	PUNCT
ejpam-3703	43	67	q1	q1	PROPN
ejpam-3703	43	68	∗q2	∗q2	PROPN
ejpam-3703	43	69	∗	∗	NOUN
ejpam-3703	43	70	s	s	NOUN
ejpam-3703	43	71	)	)	PUNCT
ejpam-3703	43	72	∗	∗	NOUN
ejpam-3703	43	73	(	(	PUNCT
ejpam-3703	43	74	s	s	PROPN
ejpam-3703	43	75	∗q1	∗q1	X
ejpam-3703	43	76	∗q2	∗q2	ADJ
ejpam-3703	43	77	)	)	PUNCT
ejpam-3703	43	78	∗	∗	NOUN
ejpam-3703	43	79	s	s	PART
ejpam-3703	43	80	∩	∩	PROPN
ejpam-3703	43	81	s	s	PART
ejpam-3703	43	82	∗	∗	NOUN
ejpam-3703	43	83	(	(	PUNCT
ejpam-3703	43	84	q1	q1	PROPN
ejpam-3703	43	85	∗q2	∗q2	ADJ
ejpam-3703	43	86	∗	∗	NOUN
ejpam-3703	43	87	s	s	NOUN
ejpam-3703	43	88	)	)	PUNCT
ejpam-3703	43	89	∗	∗	NOUN
ejpam-3703	43	90	(	(	PUNCT
ejpam-3703	43	91	s	s	X
ejpam-3703	43	92	∗q1	∗q1	X
ejpam-3703	43	93	∗q2	∗q2	ADJ
ejpam-3703	43	94	)	)	PUNCT
ejpam-3703	43	95	=	=	SYM
ejpam-3703	43	96	(	(	PUNCT
ejpam-3703	43	97	q1	q1	PROPN
ejpam-3703	43	98	∗q2	∗q2	PROPN
ejpam-3703	43	99	∗	∗	NOUN
ejpam-3703	43	100	s	s	NOUN
ejpam-3703	43	101	)	)	PUNCT
ejpam-3703	43	102	∗	∗	NOUN
ejpam-3703	43	103	(	(	PUNCT
ejpam-3703	43	104	s	s	X
ejpam-3703	43	105	∗q1	∗q1	X
ejpam-3703	43	106	∗q2	∗q2	ADJ
ejpam-3703	43	107	)	)	PUNCT
ejpam-3703	43	108	(	(	PUNCT
ejpam-3703	43	109	by	by	ADP
ejpam-3703	43	110	(	(	PUNCT
ejpam-3703	43	111	2	2	NUM
ejpam-3703	43	112	)	)	PUNCT
ejpam-3703	43	113	)	)	PUNCT
ejpam-3703	43	114	⊆	⊆	NUM
ejpam-3703	43	115	q1	q1	NOUN
ejpam-3703	43	116	∗	∗	NOUN
ejpam-3703	43	117	(	(	PUNCT
ejpam-3703	43	118	q2	q2	NOUN
ejpam-3703	43	119	∗	∗	NOUN
ejpam-3703	43	120	s	s	PART
ejpam-3703	43	121	∗q2	∗q2	ADJ
ejpam-3703	43	122	)	)	PUNCT
ejpam-3703	43	123	⊆	⊆	NUM
ejpam-3703	43	124	q1	q1	PROPN
ejpam-3703	43	125	∗	∗	NOUN
ejpam-3703	43	126	(	(	PUNCT
ejpam-3703	43	127	q2	q2	NOUN
ejpam-3703	43	128	∗	∗	NOUN
ejpam-3703	43	129	s	s	PART
ejpam-3703	43	130	∩	∩	NOUN
ejpam-3703	43	131	s	s	PART
ejpam-3703	43	132	∗q2	∗q2	ADJ
ejpam-3703	43	133	)	)	PUNCT
ejpam-3703	43	134	⊆	⊆	NUM
ejpam-3703	43	135	q1	q1	NOUN
ejpam-3703	43	136	∗q2	∗q2	PROPN
ejpam-3703	43	137	(	(	PUNCT
ejpam-3703	43	138	since	since	SCONJ
ejpam-3703	43	139	q2	q2	NOUN
ejpam-3703	43	140	is	be	AUX
ejpam-3703	43	141	a	a	DET
ejpam-3703	43	142	quasi	quasi	NOUN
ejpam-3703	43	143	-	-	NOUN
ejpam-3703	43	144	ideal	ideal	NOUN
ejpam-3703	43	145	of	of	ADP
ejpam-3703	43	146	s	s	NOUN
ejpam-3703	43	147	)	)	PUNCT
ejpam-3703	43	148	.	.	PUNCT
ejpam-3703	44	1	hence	hence	ADV
ejpam-3703	44	2	q1	q1	PROPN
ejpam-3703	44	3	∗q2	∗q2	PROPN
ejpam-3703	44	4	is	be	AUX
ejpam-3703	44	5	a	a	DET
ejpam-3703	44	6	quasi	quasi	NOUN
ejpam-3703	44	7	-	-	NOUN
ejpam-3703	44	8	ideal	ideal	NOUN
ejpam-3703	44	9	of	of	ADP
ejpam-3703	44	10	s.	s.	PROPN
ejpam-3703	44	11	thus	thus	ADV
ejpam-3703	44	12	(	(	PUNCT
ejpam-3703	44	13	q	q	X
ejpam-3703	44	14	,	,	PUNCT
ejpam-3703	44	15	∗	∗	NOUN
ejpam-3703	44	16	)	)	PUNCT
ejpam-3703	44	17	is	be	AUX
ejpam-3703	44	18	semigroup	semigroup	ADJ
ejpam-3703	44	19	.	.	PUNCT
ejpam-3703	45	1	the	the	DET
ejpam-3703	45	2	semigroup	semigroup	NOUN
ejpam-3703	45	3	(	(	PUNCT
ejpam-3703	45	4	q	q	INTJ
ejpam-3703	45	5	,	,	PUNCT
ejpam-3703	45	6	∗	∗	NOUN
ejpam-3703	45	7	)	)	PUNCT
ejpam-3703	45	8	is	be	AUX
ejpam-3703	45	9	a	a	DET
ejpam-3703	45	10	von	von	PROPN
ejpam-3703	45	11	neumann	neumann	PROPN
ejpam-3703	45	12	regular	regular	PROPN
ejpam-3703	45	13	semigroup	semigroup	PROPN
ejpam-3703	45	14	.	.	PUNCT
ejpam-3703	46	1	in	in	ADP
ejpam-3703	46	2	fact	fact	NOUN
ejpam-3703	46	3	:	:	PUNCT
ejpam-3703	46	4	let	let	VERB
ejpam-3703	46	5	q	q	PROPN
ejpam-3703	46	6	∈	∈	PROPN
ejpam-3703	46	7	q.	q.	NOUN
ejpam-3703	46	8	since	since	SCONJ
ejpam-3703	46	9	(	(	PUNCT
ejpam-3703	46	10	s	s	X
ejpam-3703	46	11	,	,	PUNCT
ejpam-3703	46	12	◦	◦	NOUN
ejpam-3703	46	13	)	)	PUNCT
ejpam-3703	46	14	is	be	AUX
ejpam-3703	46	15	regular	regular	ADJ
ejpam-3703	46	16	,	,	PUNCT
ejpam-3703	46	17	by	by	ADP
ejpam-3703	46	18	lemma	lemma	PROPN
ejpam-3703	46	19	2	2	NUM
ejpam-3703	46	20	,	,	PUNCT
ejpam-3703	46	21	we	we	PRON
ejpam-3703	46	22	have	have	VERB
ejpam-3703	46	23	q	q	NOUN
ejpam-3703	46	24	⊆	⊆	NUM
ejpam-3703	46	25	q	q	PUNCT
ejpam-3703	46	26	∗	∗	PRON
ejpam-3703	46	27	s	s	PART
ejpam-3703	46	28	∗q	∗q	PROPN
ejpam-3703	46	29	⊆	⊆	NUM
ejpam-3703	46	30	(	(	PUNCT
ejpam-3703	46	31	q	q	NOUN
ejpam-3703	46	32	∗	∗	NUM
ejpam-3703	46	33	s	s	NOUN
ejpam-3703	46	34	)	)	PUNCT
ejpam-3703	46	35	∩	∩	NOUN
ejpam-3703	46	36	(	(	PUNCT
ejpam-3703	46	37	s	s	PROPN
ejpam-3703	46	38	∗q	∗q	PROPN
ejpam-3703	46	39	)	)	PUNCT
ejpam-3703	46	40	⊆	⊆	NUM
ejpam-3703	46	41	q.	q.	NOUN
ejpam-3703	46	42	then	then	ADV
ejpam-3703	46	43	q	q	PROPN
ejpam-3703	46	44	=	=	PUNCT
ejpam-3703	46	45	q	q	NOUN
ejpam-3703	46	46	∗	∗	PRON
ejpam-3703	46	47	s	s	PART
ejpam-3703	46	48	∗q	∗q	NOUN
ejpam-3703	46	49	,	,	PUNCT
ejpam-3703	46	50	where	where	SCONJ
ejpam-3703	46	51	s	s	VERB
ejpam-3703	46	52	∈	∈	PROPN
ejpam-3703	46	53	q	q	X
ejpam-3703	46	54	and	and	CCONJ
ejpam-3703	46	55	so	so	ADV
ejpam-3703	46	56	(	(	PUNCT
ejpam-3703	46	57	q	q	X
ejpam-3703	46	58	,	,	PUNCT
ejpam-3703	46	59	∗	∗	NOUN
ejpam-3703	46	60	)	)	PUNCT
ejpam-3703	46	61	is	be	AUX
ejpam-3703	46	62	a	a	DET
ejpam-3703	46	63	von	von	PROPN
ejpam-3703	46	64	neumann	neumann	PROPN
ejpam-3703	46	65	regular	regular	PROPN
ejpam-3703	46	66	semigroup	semigroup	PROPN
ejpam-3703	46	67	.	.	PUNCT
ejpam-3703	47	1	⇐	⇐	PROPN
ejpam-3703	47	2	=	=	PROPN
ejpam-3703	47	3	.	.	PUNCT
ejpam-3703	48	1	we	we	PRON
ejpam-3703	48	2	remark	remark	VERB
ejpam-3703	48	3	first	first	ADV
ejpam-3703	48	4	that	that	SCONJ
ejpam-3703	48	5	for	for	ADP
ejpam-3703	48	6	each	each	DET
ejpam-3703	48	7	quasi	quasi	ADJ
ejpam-3703	48	8	-	-	ADJ
ejpam-3703	48	9	ideal	ideal	ADJ
ejpam-3703	48	10	q	q	NOUN
ejpam-3703	48	11	of	of	ADP
ejpam-3703	48	12	s	s	PROPN
ejpam-3703	48	13	,	,	PUNCT
ejpam-3703	48	14	we	we	PRON
ejpam-3703	48	15	have	have	VERB
ejpam-3703	48	16	q	q	NOUN
ejpam-3703	48	17	=	=	PUNCT
ejpam-3703	48	18	q	q	NOUN
ejpam-3703	48	19	∗	∗	PRON
ejpam-3703	48	20	s	s	PART
ejpam-3703	48	21	∗q	∗q	PROPN
ejpam-3703	48	22	(	(	PUNCT
ejpam-3703	48	23	3	3	NUM
ejpam-3703	48	24	)	)	PUNCT
ejpam-3703	48	25	in	in	ADP
ejpam-3703	48	26	fact	fact	NOUN
ejpam-3703	48	27	:	:	PUNCT
ejpam-3703	48	28	let	let	VERB
ejpam-3703	48	29	q	q	PART
ejpam-3703	48	30	be	be	AUX
ejpam-3703	48	31	a	a	DET
ejpam-3703	48	32	quasi	quasi	NOUN
ejpam-3703	48	33	-	-	NOUN
ejpam-3703	48	34	ideal	ideal	NOUN
ejpam-3703	48	35	of	of	ADP
ejpam-3703	48	36	s.	s.	PROPN
ejpam-3703	48	37	since	since	SCONJ
ejpam-3703	48	38	(	(	PUNCT
ejpam-3703	48	39	q	q	INTJ
ejpam-3703	48	40	,	,	PUNCT
ejpam-3703	48	41	∗	∗	NOUN
ejpam-3703	48	42	)	)	PUNCT
ejpam-3703	48	43	is	be	AUX
ejpam-3703	48	44	von	von	PROPN
ejpam-3703	48	45	neumann	neumann	PROPN
ejpam-3703	48	46	regular	regular	PROPN
ejpam-3703	48	47	semigroup	semigroup	PROPN
ejpam-3703	48	48	,	,	PUNCT
ejpam-3703	48	49	there	there	PRON
ejpam-3703	48	50	exists	exist	VERB
ejpam-3703	48	51	x	x	X
ejpam-3703	48	52	∈	∈	PROPN
ejpam-3703	48	53	q	q	NOUN
ejpam-3703	48	54	such	such	ADJ
ejpam-3703	48	55	that	that	DET
ejpam-3703	48	56	q	q	NOUN
ejpam-3703	48	57	=	=	PUNCT
ejpam-3703	48	58	q	q	PUNCT
ejpam-3703	48	59	∗x	∗x	ADJ
ejpam-3703	48	60	∗q	∗q	PROPN
ejpam-3703	48	61	.	.	PUNCT
ejpam-3703	49	1	then	then	ADV
ejpam-3703	49	2	q	q	X
ejpam-3703	49	3	=	=	PUNCT
ejpam-3703	49	4	q	q	PUNCT
ejpam-3703	49	5	∗x	∗x	PRON
ejpam-3703	49	6	∗q	∗q	NOUN
ejpam-3703	50	1	⊆	⊆	NUM
ejpam-3703	50	2	q	q	NOUN
ejpam-3703	50	3	∗	∗	PRON
ejpam-3703	50	4	s	s	PART
ejpam-3703	50	5	∗q	∗q	PROPN
ejpam-3703	50	6	⊆	⊆	NUM
ejpam-3703	50	7	(	(	PUNCT
ejpam-3703	50	8	q	q	NOUN
ejpam-3703	50	9	∗	∗	NUM
ejpam-3703	50	10	s	s	NOUN
ejpam-3703	50	11	)	)	PUNCT
ejpam-3703	50	12	∩	∩	NOUN
ejpam-3703	50	13	(	(	PUNCT
ejpam-3703	50	14	s	s	PROPN
ejpam-3703	50	15	∗q	∗q	PROPN
ejpam-3703	50	16	)	)	PUNCT
ejpam-3703	50	17	⊆	⊆	NUM
ejpam-3703	50	18	q.	q.	NOUN
ejpam-3703	50	19	thus	thus	ADV
ejpam-3703	50	20	we	we	PRON
ejpam-3703	50	21	have	have	VERB
ejpam-3703	50	22	q	q	NOUN
ejpam-3703	50	23	=	=	PUNCT
ejpam-3703	50	24	q	q	NOUN
ejpam-3703	50	25	∗	∗	PRON
ejpam-3703	50	26	s	s	PART
ejpam-3703	50	27	∗q	∗q	PROPN
ejpam-3703	50	28	and	and	CCONJ
ejpam-3703	50	29	property	property	NOUN
ejpam-3703	50	30	(	(	PUNCT
ejpam-3703	50	31	3	3	X
ejpam-3703	50	32	)	)	PUNCT
ejpam-3703	50	33	holds	hold	VERB
ejpam-3703	50	34	.	.	PUNCT
ejpam-3703	51	1	we	we	PRON
ejpam-3703	51	2	are	be	AUX
ejpam-3703	51	3	ready	ready	ADJ
ejpam-3703	51	4	now	now	ADV
ejpam-3703	51	5	to	to	PART
ejpam-3703	51	6	prove	prove	VERB
ejpam-3703	51	7	that	that	SCONJ
ejpam-3703	51	8	(	(	PUNCT
ejpam-3703	51	9	s	s	NOUN
ejpam-3703	51	10	,	,	PUNCT
ejpam-3703	51	11	◦	◦	NOUN
ejpam-3703	51	12	)	)	PUNCT
ejpam-3703	51	13	is	be	AUX
ejpam-3703	51	14	regular	regular	ADJ
ejpam-3703	51	15	.	.	PUNCT
ejpam-3703	52	1	for	for	ADP
ejpam-3703	52	2	this	this	PRON
ejpam-3703	52	3	,	,	PUNCT
ejpam-3703	52	4	let	let	VERB
ejpam-3703	52	5	a	a	PRON
ejpam-3703	52	6	be	be	AUX
ejpam-3703	52	7	a	a	DET
ejpam-3703	52	8	nonempty	nonempty	ADJ
ejpam-3703	52	9	subset	subset	NOUN
ejpam-3703	52	10	of	of	ADP
ejpam-3703	52	11	s.	s.	PROPN
ejpam-3703	52	12	by	by	ADP
ejpam-3703	52	13	lemma	lemma	PROPN
ejpam-3703	52	14	2	2	NUM
ejpam-3703	52	15	,	,	PUNCT
ejpam-3703	52	16	it	it	PRON
ejpam-3703	52	17	is	be	AUX
ejpam-3703	52	18	enough	enough	ADJ
ejpam-3703	52	19	to	to	PART
ejpam-3703	52	20	prove	prove	VERB
ejpam-3703	52	21	that	that	SCONJ
ejpam-3703	52	22	a	a	DET
ejpam-3703	52	23	⊆	⊆	NUM
ejpam-3703	52	24	a	a	DET
ejpam-3703	52	25	∗	∗	NOUN
ejpam-3703	52	26	s	s	NOUN
ejpam-3703	52	27	∗a	∗a	PROPN
ejpam-3703	52	28	.	.	PUNCT
ejpam-3703	53	1	since	since	SCONJ
ejpam-3703	53	2	r(a	r(a	PROPN
ejpam-3703	53	3	)	)	PUNCT
ejpam-3703	53	4	is	be	AUX
ejpam-3703	53	5	a	a	DET
ejpam-3703	53	6	right	right	ADJ
ejpam-3703	53	7	ideal	ideal	NOUN
ejpam-3703	53	8	and	and	CCONJ
ejpam-3703	53	9	l(a	l(a	PROPN
ejpam-3703	53	10	)	)	PUNCT
ejpam-3703	54	1	is	be	AUX
ejpam-3703	54	2	a	a	DET
ejpam-3703	54	3	left	left	ADJ
ejpam-3703	54	4	ideal	ideal	NOUN
ejpam-3703	54	5	of	of	ADP
ejpam-3703	54	6	s	s	PROPN
ejpam-3703	54	7	,	,	PUNCT
ejpam-3703	54	8	by	by	ADP
ejpam-3703	54	9	lemma	lemma	PROPN
ejpam-3703	54	10	3	3	NUM
ejpam-3703	54	11	,	,	PUNCT
ejpam-3703	54	12	r(a	r(a	NUM
ejpam-3703	54	13	)	)	PUNCT
ejpam-3703	54	14	∩	∩	NOUN
ejpam-3703	54	15	l(a	l(a	PROPN
ejpam-3703	54	16	)	)	PUNCT
ejpam-3703	55	1	is	be	AUX
ejpam-3703	55	2	a	a	DET
ejpam-3703	55	3	quasi	quasi	NOUN
ejpam-3703	55	4	-	-	NOUN
ejpam-3703	55	5	ideal	ideal	NOUN
ejpam-3703	55	6	of	of	ADP
ejpam-3703	55	7	s.	s.	PROPN
ejpam-3703	55	8	then	then	ADV
ejpam-3703	55	9	,	,	PUNCT
ejpam-3703	55	10	by	by	ADP
ejpam-3703	55	11	(	(	PUNCT
ejpam-3703	55	12	3	3	NUM
ejpam-3703	55	13	)	)	PUNCT
ejpam-3703	55	14	,	,	PUNCT
ejpam-3703	55	15	we	we	PRON
ejpam-3703	55	16	have	have	VERB
ejpam-3703	55	17	a	a	DET
ejpam-3703	55	18	⊆	⊆	NUM
ejpam-3703	55	19	r(a	r(a	NUM
ejpam-3703	55	20	)	)	PUNCT
ejpam-3703	55	21	∩	∩	NOUN
ejpam-3703	55	22	l(a	l(a	PROPN
ejpam-3703	55	23	)	)	PUNCT
ejpam-3703	56	1	=	=	PRON
ejpam-3703	56	2	(	(	PUNCT
ejpam-3703	56	3	r(a	r(a	PROPN
ejpam-3703	56	4	)	)	PUNCT
ejpam-3703	56	5	∩	∩	NOUN
ejpam-3703	56	6	l(a	l(a	PROPN
ejpam-3703	56	7	)	)	PUNCT
ejpam-3703	56	8	)	)	PUNCT
ejpam-3703	57	1	∗	∗	NOUN
ejpam-3703	57	2	s	s	PART
ejpam-3703	57	3	∗	∗	NOUN
ejpam-3703	57	4	(	(	PUNCT
ejpam-3703	57	5	r(a	r(a	PROPN
ejpam-3703	57	6	)	)	PUNCT
ejpam-3703	57	7	∩	∩	NOUN
ejpam-3703	57	8	l(a	l(a	PROPN
ejpam-3703	57	9	)	)	PUNCT
ejpam-3703	57	10	)	)	PUNCT
ejpam-3703	58	1	⊆	⊆	NUM
ejpam-3703	58	2	(	(	PUNCT
ejpam-3703	58	3	r(a	r(a	NUM
ejpam-3703	58	4	)	)	PUNCT
ejpam-3703	58	5	∗	∗	NOUN
ejpam-3703	58	6	s	s	PART
ejpam-3703	58	7	)	)	PUNCT
ejpam-3703	58	8	∗	∗	NOUN
ejpam-3703	58	9	l(a	l(a	PROPN
ejpam-3703	58	10	)	)	PUNCT
ejpam-3703	58	11	⊆	⊆	NUM
ejpam-3703	58	12	r(a	r(a	NUM
ejpam-3703	58	13	)	)	PUNCT
ejpam-3703	58	14	∗	∗	NOUN
ejpam-3703	58	15	l(a	l(a	PROPN
ejpam-3703	58	16	)	)	PUNCT
ejpam-3703	58	17	=	=	PRON
ejpam-3703	58	18	(	(	PUNCT
ejpam-3703	58	19	a	a	DET
ejpam-3703	58	20	∪	∪	X
ejpam-3703	58	21	(	(	PUNCT
ejpam-3703	58	22	a	a	DET
ejpam-3703	58	23	∗	∗	NOUN
ejpam-3703	58	24	s	s	NOUN
ejpam-3703	58	25	)	)	PUNCT
ejpam-3703	58	26	)	)	PUNCT
ejpam-3703	58	27	∗	∗	NOUN
ejpam-3703	58	28	(	(	PUNCT
ejpam-3703	58	29	a	a	DET
ejpam-3703	58	30	∪	∪	ADJ
ejpam-3703	58	31	(	(	PUNCT
ejpam-3703	58	32	s	s	NOUN
ejpam-3703	58	33	∗a	∗a	ADJ
ejpam-3703	58	34	)	)	PUNCT
ejpam-3703	58	35	)	)	PUNCT
ejpam-3703	59	1	n.	n.	NOUN
ejpam-3703	59	2	kehayopulu	kehayopulu	PROPN
ejpam-3703	59	3	/	/	SYM
ejpam-3703	59	4	eur	eur	PROPN
ejpam-3703	59	5	.	.	PUNCT
ejpam-3703	60	1	j.	j.	PROPN
ejpam-3703	60	2	pure	pure	PROPN
ejpam-3703	60	3	appl	appl	PROPN
ejpam-3703	60	4	.	.	PROPN
ejpam-3703	60	5	math	math	PROPN
ejpam-3703	60	6	,	,	PUNCT
ejpam-3703	60	7	13	13	NUM
ejpam-3703	60	8	(	(	PUNCT
ejpam-3703	60	9	2	2	NUM
ejpam-3703	60	10	)	)	PUNCT
ejpam-3703	60	11	(	(	PUNCT
ejpam-3703	60	12	2020	2020	NUM
ejpam-3703	60	13	)	)	PUNCT
ejpam-3703	60	14	,	,	PUNCT
ejpam-3703	60	15	346	346	NUM
ejpam-3703	60	16	-	-	SYM
ejpam-3703	60	17	350	350	NUM
ejpam-3703	60	18	349	349	NUM
ejpam-3703	60	19	=	=	NOUN
ejpam-3703	60	20	a	a	DET
ejpam-3703	60	21	∗a	∗a	ADJ
ejpam-3703	60	22	∪a	∪a	X
ejpam-3703	60	23	∗	∗	NOUN
ejpam-3703	60	24	s	s	PART
ejpam-3703	60	25	∗a	∗a	ADJ
ejpam-3703	60	26	∪a	∪a	X
ejpam-3703	60	27	∗	∗	NOUN
ejpam-3703	60	28	s	s	PART
ejpam-3703	60	29	∗	∗	NOUN
ejpam-3703	60	30	s	s	NOUN
ejpam-3703	60	31	∗a	∗a	PROPN
ejpam-3703	60	32	=	=	SYM
ejpam-3703	60	33	a	a	DET
ejpam-3703	60	34	∗a	∗a	ADJ
ejpam-3703	60	35	∪a	∪a	X
ejpam-3703	60	36	∗	∗	NOUN
ejpam-3703	60	37	s	s	NOUN
ejpam-3703	60	38	∗a	∗a	ADJ
ejpam-3703	60	39	,	,	PUNCT
ejpam-3703	60	40	then	then	ADV
ejpam-3703	60	41	a	a	DET
ejpam-3703	60	42	∗a	∗a	ADJ
ejpam-3703	60	43	⊆	⊆	NUM
ejpam-3703	60	44	a	a	DET
ejpam-3703	60	45	∗a	∗a	ADJ
ejpam-3703	60	46	∗a	∗a	ADJ
ejpam-3703	60	47	∪a	∪a	X
ejpam-3703	60	48	∗	∗	NOUN
ejpam-3703	60	49	s	s	PART
ejpam-3703	60	50	∗a	∗a	ADJ
ejpam-3703	60	51	∗a	∗a	ADJ
ejpam-3703	60	52	⊆	⊆	PROPN
ejpam-3703	60	53	a	a	DET
ejpam-3703	60	54	∗	∗	NOUN
ejpam-3703	60	55	s	s	NOUN
ejpam-3703	60	56	∗a	∗a	ADJ
ejpam-3703	60	57	,	,	PUNCT
ejpam-3703	60	58	thus	thus	ADV
ejpam-3703	60	59	we	we	PRON
ejpam-3703	60	60	obtain	obtain	VERB
ejpam-3703	60	61	a	a	DET
ejpam-3703	60	62	⊆	⊆	NUM
ejpam-3703	60	63	a	a	DET
ejpam-3703	60	64	∗	∗	NOUN
ejpam-3703	60	65	s	s	NOUN
ejpam-3703	60	66	∗a	∗a	ADJ
ejpam-3703	60	67	and	and	CCONJ
ejpam-3703	60	68	so	so	ADV
ejpam-3703	60	69	the	the	DET
ejpam-3703	60	70	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	60	71	(	(	PUNCT
ejpam-3703	60	72	s	s	NOUN
ejpam-3703	60	73	,	,	PUNCT
ejpam-3703	60	74	◦	◦	NOUN
ejpam-3703	60	75	)	)	PUNCT
ejpam-3703	60	76	is	be	AUX
ejpam-3703	60	77	regular	regular	ADJ
ejpam-3703	60	78	.	.	PUNCT
ejpam-3703	61	1	�	�	PROPN
ejpam-3703	61	2	lemma	lemma	PROPN
ejpam-3703	61	3	7	7	NUM
ejpam-3703	62	1	[	[	X
ejpam-3703	62	2	4	4	NUM
ejpam-3703	62	3	,	,	PUNCT
ejpam-3703	62	4	5	5	NUM
ejpam-3703	62	5	]	]	PUNCT
ejpam-3703	62	6	an	an	DET
ejpam-3703	62	7	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	62	8	(	(	PUNCT
ejpam-3703	62	9	s	s	NOUN
ejpam-3703	62	10	,	,	PUNCT
ejpam-3703	62	11	◦	◦	NOUN
ejpam-3703	62	12	)	)	PUNCT
ejpam-3703	62	13	is	be	AUX
ejpam-3703	62	14	intra	intra	ADJ
ejpam-3703	62	15	-	-	ADJ
ejpam-3703	62	16	regular	regular	ADJ
ejpam-3703	62	17	if	if	SCONJ
ejpam-3703	62	18	and	and	CCONJ
ejpam-3703	62	19	only	only	ADV
ejpam-3703	62	20	if	if	SCONJ
ejpam-3703	62	21	,	,	PUNCT
ejpam-3703	62	22	for	for	ADP
ejpam-3703	62	23	every	every	DET
ejpam-3703	62	24	right	right	ADJ
ejpam-3703	62	25	ideal	ideal	NOUN
ejpam-3703	62	26	a	a	PRON
ejpam-3703	62	27	and	and	CCONJ
ejpam-3703	62	28	every	every	PRON
ejpam-3703	62	29	left	leave	VERB
ejpam-3703	62	30	ideal	ideal	PROPN
ejpam-3703	62	31	b	b	PROPN
ejpam-3703	62	32	of	of	ADP
ejpam-3703	62	33	s	s	PROPN
ejpam-3703	62	34	,	,	PUNCT
ejpam-3703	62	35	we	we	PRON
ejpam-3703	62	36	have	have	VERB
ejpam-3703	62	37	a	a	DET
ejpam-3703	62	38	∩b	∩b	NOUN
ejpam-3703	62	39	⊆	⊆	NUM
ejpam-3703	62	40	b	b	NOUN
ejpam-3703	62	41	∗a	∗a	NOUN
ejpam-3703	62	42	.	.	PUNCT
ejpam-3703	63	1	an	an	DET
ejpam-3703	63	2	element	element	NOUN
ejpam-3703	63	3	a	a	PRON
ejpam-3703	63	4	of	of	ADP
ejpam-3703	63	5	a	a	DET
ejpam-3703	63	6	semigroup	semigroup	NOUN
ejpam-3703	63	7	s	s	PART
ejpam-3703	63	8	is	be	AUX
ejpam-3703	63	9	called	call	VERB
ejpam-3703	63	10	idempotent	idempotent	ADJ
ejpam-3703	63	11	if	if	SCONJ
ejpam-3703	63	12	a2	a2	PROPN
ejpam-3703	63	13	=	=	PUNCT
ejpam-3703	63	14	a.	a.	NOUN
ejpam-3703	63	15	an	an	DET
ejpam-3703	63	16	idempotent	idempotent	ADJ
ejpam-3703	63	17	semigroup	semigroup	NOUN
ejpam-3703	63	18	or	or	CCONJ
ejpam-3703	63	19	shorter	short	ADJ
ejpam-3703	63	20	a	a	DET
ejpam-3703	63	21	band	band	NOUN
ejpam-3703	63	22	is	be	AUX
ejpam-3703	63	23	a	a	DET
ejpam-3703	63	24	semigroup	semigroup	NOUN
ejpam-3703	63	25	in	in	ADP
ejpam-3703	63	26	which	which	PRON
ejpam-3703	63	27	all	all	DET
ejpam-3703	63	28	elements	element	NOUN
ejpam-3703	63	29	are	be	AUX
ejpam-3703	63	30	idempotent	idempotent	ADJ
ejpam-3703	63	31	.	.	PUNCT
ejpam-3703	64	1	theorem	theorem	ADJ
ejpam-3703	64	2	8	8	NUM
ejpam-3703	64	3	let	let	VERB
ejpam-3703	64	4	(	(	PUNCT
ejpam-3703	64	5	s	s	NOUN
ejpam-3703	64	6	,	,	PUNCT
ejpam-3703	64	7	◦	◦	NOUN
ejpam-3703	64	8	)	)	PUNCT
ejpam-3703	64	9	is	be	AUX
ejpam-3703	64	10	an	an	DET
ejpam-3703	64	11	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	64	12	.	.	PUNCT
ejpam-3703	65	1	if	if	SCONJ
ejpam-3703	65	2	(	(	PUNCT
ejpam-3703	65	3	s	s	NOUN
ejpam-3703	65	4	,	,	PUNCT
ejpam-3703	65	5	◦	◦	NOUN
ejpam-3703	65	6	)	)	PUNCT
ejpam-3703	65	7	is	be	AUX
ejpam-3703	65	8	both	both	CCONJ
ejpam-3703	65	9	regular	regular	ADJ
ejpam-3703	65	10	and	and	CCONJ
ejpam-3703	65	11	intra	intra	ADJ
ejpam-3703	65	12	-	-	ADJ
ejpam-3703	65	13	regular	regular	ADJ
ejpam-3703	65	14	,	,	PUNCT
ejpam-3703	65	15	then	then	ADV
ejpam-3703	65	16	the	the	DET
ejpam-3703	65	17	set	set	NOUN
ejpam-3703	65	18	q	q	NOUN
ejpam-3703	65	19	of	of	ADP
ejpam-3703	65	20	all	all	DET
ejpam-3703	65	21	quasi	quasi	NOUN
ejpam-3703	65	22	-	-	NOUN
ejpam-3703	65	23	ideals	ideal	NOUN
ejpam-3703	65	24	of	of	ADP
ejpam-3703	65	25	s	s	NOUN
ejpam-3703	65	26	with	with	ADP
ejpam-3703	65	27	the	the	DET
ejpam-3703	65	28	operation	operation	NOUN
ejpam-3703	65	29	“	"	PUNCT
ejpam-3703	65	30	∗	∗	NOUN
ejpam-3703	65	31	”	"	PUNCT
ejpam-3703	65	32	is	be	AUX
ejpam-3703	65	33	a	a	DET
ejpam-3703	65	34	band	band	NOUN
ejpam-3703	65	35	.	.	PUNCT
ejpam-3703	66	1	“	"	PUNCT
ejpam-3703	66	2	conversely	conversely	ADV
ejpam-3703	66	3	”	"	PUNCT
ejpam-3703	66	4	,	,	PUNCT
ejpam-3703	66	5	if	if	SCONJ
ejpam-3703	66	6	the	the	DET
ejpam-3703	66	7	quasi	quasi	NOUN
ejpam-3703	66	8	-	-	NOUN
ejpam-3703	66	9	ideals	ideal	NOUN
ejpam-3703	66	10	of	of	ADP
ejpam-3703	66	11	(	(	PUNCT
ejpam-3703	66	12	s	s	X
ejpam-3703	66	13	,	,	PUNCT
ejpam-3703	66	14	◦	◦	NOUN
ejpam-3703	66	15	)	)	PUNCT
ejpam-3703	66	16	are	be	AUX
ejpam-3703	66	17	idempotent	idempotent	ADJ
ejpam-3703	66	18	,	,	PUNCT
ejpam-3703	66	19	then	then	ADV
ejpam-3703	66	20	s	s	VERB
ejpam-3703	66	21	is	be	AUX
ejpam-3703	66	22	both	both	PRON
ejpam-3703	66	23	regular	regular	ADJ
ejpam-3703	66	24	and	and	CCONJ
ejpam-3703	66	25	intra	intra	ADJ
ejpam-3703	66	26	-	-	ADJ
ejpam-3703	66	27	regular	regular	ADJ
ejpam-3703	66	28	.	.	PUNCT
ejpam-3703	67	1	proof	proof	NOUN
ejpam-3703	67	2	=	=	PRON
ejpam-3703	67	3	⇒.	⇒.	PRON
ejpam-3703	67	4	let	let	VERB
ejpam-3703	67	5	(	(	PUNCT
ejpam-3703	67	6	s	s	NOUN
ejpam-3703	67	7	,	,	PUNCT
ejpam-3703	67	8	◦	◦	NOUN
ejpam-3703	67	9	)	)	PUNCT
ejpam-3703	67	10	be	be	VERB
ejpam-3703	67	11	both	both	ADV
ejpam-3703	67	12	regular	regular	ADJ
ejpam-3703	67	13	and	and	CCONJ
ejpam-3703	67	14	intra	intra	ADJ
ejpam-3703	67	15	-	-	ADJ
ejpam-3703	67	16	regular	regular	ADJ
ejpam-3703	67	17	.	.	PUNCT
ejpam-3703	68	1	since	since	SCONJ
ejpam-3703	68	2	(	(	PUNCT
ejpam-3703	68	3	s	s	X
ejpam-3703	68	4	,	,	PUNCT
ejpam-3703	68	5	◦	◦	NOUN
ejpam-3703	68	6	)	)	PUNCT
ejpam-3703	68	7	is	be	AUX
ejpam-3703	68	8	regular	regular	ADJ
ejpam-3703	68	9	,	,	PUNCT
ejpam-3703	68	10	by	by	ADP
ejpam-3703	68	11	theorem	theorem	NOUN
ejpam-3703	68	12	6	6	NUM
ejpam-3703	68	13	,	,	PUNCT
ejpam-3703	68	14	(	(	PUNCT
ejpam-3703	68	15	q	q	INTJ
ejpam-3703	68	16	,	,	PUNCT
ejpam-3703	68	17	∗	∗	NOUN
ejpam-3703	68	18	)	)	PUNCT
ejpam-3703	68	19	is	be	AUX
ejpam-3703	68	20	a	a	DET
ejpam-3703	68	21	semigroup	semigroup	NOUN
ejpam-3703	68	22	.	.	PUNCT
ejpam-3703	69	1	moreover	moreover	ADV
ejpam-3703	69	2	,	,	PUNCT
ejpam-3703	69	3	the	the	DET
ejpam-3703	69	4	elements	element	NOUN
ejpam-3703	69	5	of	of	ADP
ejpam-3703	69	6	the	the	DET
ejpam-3703	69	7	semigroup	semigroup	PROPN
ejpam-3703	69	8	q	q	NOUN
ejpam-3703	69	9	are	be	AUX
ejpam-3703	69	10	idempotent	idempotent	ADJ
ejpam-3703	69	11	.	.	PUNCT
ejpam-3703	70	1	in	in	ADP
ejpam-3703	70	2	fact	fact	NOUN
ejpam-3703	70	3	:	:	PUNCT
ejpam-3703	70	4	let	let	VERB
ejpam-3703	70	5	q	q	PART
ejpam-3703	70	6	be	be	AUX
ejpam-3703	70	7	a	a	DET
ejpam-3703	70	8	quasi	quasi	NOUN
ejpam-3703	70	9	-	-	NOUN
ejpam-3703	70	10	ideal	ideal	NOUN
ejpam-3703	70	11	of	of	ADP
ejpam-3703	70	12	s.	s.	PROPN
ejpam-3703	70	13	since	since	SCONJ
ejpam-3703	70	14	s	s	PROPN
ejpam-3703	70	15	is	be	AUX
ejpam-3703	70	16	regular	regular	ADJ
ejpam-3703	70	17	,	,	PUNCT
ejpam-3703	70	18	we	we	PRON
ejpam-3703	70	19	have	have	VERB
ejpam-3703	70	20	q	q	NOUN
ejpam-3703	70	21	=	=	PUNCT
ejpam-3703	70	22	q	q	NOUN
ejpam-3703	70	23	∗	∗	X
ejpam-3703	70	24	s	s	NOUN
ejpam-3703	70	25	∗	∗	NOUN
ejpam-3703	70	26	q	q	PROPN
ejpam-3703	70	27	(	(	PUNCT
ejpam-3703	70	28	cf	cf	NOUN
ejpam-3703	70	29	.	.	PUNCT
ejpam-3703	71	1	the	the	DET
ejpam-3703	71	2	proof	proof	NOUN
ejpam-3703	71	3	of	of	ADP
ejpam-3703	71	4	theorem	theorem	NOUN
ejpam-3703	71	5	6	6	NUM
ejpam-3703	71	6	)	)	PUNCT
ejpam-3703	71	7	.	.	PUNCT
ejpam-3703	72	1	hence	hence	ADV
ejpam-3703	72	2	we	we	PRON
ejpam-3703	72	3	have	have	VERB
ejpam-3703	72	4	q	q	NOUN
ejpam-3703	72	5	=	=	PUNCT
ejpam-3703	72	6	q	q	NOUN
ejpam-3703	72	7	∗	∗	PRON
ejpam-3703	72	8	s	s	PART
ejpam-3703	72	9	∗q	∗q	NOUN
ejpam-3703	72	10	=	=	PUNCT
ejpam-3703	72	11	(	(	PUNCT
ejpam-3703	72	12	q	q	NOUN
ejpam-3703	72	13	∗	∗	X
ejpam-3703	72	14	s	s	PART
ejpam-3703	72	15	∗q	∗q	NOUN
ejpam-3703	72	16	)	)	PUNCT
ejpam-3703	72	17	∗	∗	NOUN
ejpam-3703	72	18	s	s	PART
ejpam-3703	72	19	∗	∗	NOUN
ejpam-3703	72	20	(	(	PUNCT
ejpam-3703	72	21	q	q	NOUN
ejpam-3703	72	22	∗	∗	X
ejpam-3703	72	23	s	s	PART
ejpam-3703	72	24	∗q	∗q	NOUN
ejpam-3703	72	25	)	)	PUNCT
ejpam-3703	72	26	=	=	PUNCT
ejpam-3703	73	1	(	(	PUNCT
ejpam-3703	73	2	q	q	NOUN
ejpam-3703	73	3	∗	∗	X
ejpam-3703	73	4	s	s	PART
ejpam-3703	73	5	∗q	∗q	NOUN
ejpam-3703	73	6	)	)	PUNCT
ejpam-3703	73	7	∗	∗	NOUN
ejpam-3703	73	8	s	s	PART
ejpam-3703	73	9	∗	∗	NOUN
ejpam-3703	73	10	s	s	PART
ejpam-3703	73	11	∗	∗	NOUN
ejpam-3703	73	12	(	(	PUNCT
ejpam-3703	73	13	q	q	NOUN
ejpam-3703	73	14	∗	∗	X
ejpam-3703	73	15	s	s	PART
ejpam-3703	73	16	∗q	∗q	NOUN
ejpam-3703	73	17	)	)	PUNCT
ejpam-3703	73	18	(	(	PUNCT
ejpam-3703	73	19	by	by	ADP
ejpam-3703	73	20	lemma	lemma	PROPN
ejpam-3703	73	21	5	5	NUM
ejpam-3703	73	22	)	)	PUNCT
ejpam-3703	73	23	=	=	PUNCT
ejpam-3703	73	24	(	(	PUNCT
ejpam-3703	73	25	q	q	NOUN
ejpam-3703	73	26	∗	∗	X
ejpam-3703	73	27	s	s	NOUN
ejpam-3703	73	28	)	)	PUNCT
ejpam-3703	73	29	∗	∗	NOUN
ejpam-3703	73	30	(	(	PUNCT
ejpam-3703	73	31	q	q	NOUN
ejpam-3703	73	32	∗	∗	X
ejpam-3703	73	33	s	s	NOUN
ejpam-3703	73	34	)	)	PUNCT
ejpam-3703	73	35	∗	∗	NOUN
ejpam-3703	73	36	(	(	PUNCT
ejpam-3703	73	37	s	s	X
ejpam-3703	73	38	∗q	∗q	PROPN
ejpam-3703	73	39	)	)	PUNCT
ejpam-3703	73	40	∗	∗	NOUN
ejpam-3703	73	41	(	(	PUNCT
ejpam-3703	73	42	s	s	X
ejpam-3703	73	43	∗q	∗q	PROPN
ejpam-3703	73	44	)	)	PUNCT
ejpam-3703	73	45	.	.	PUNCT
ejpam-3703	74	1	since	since	SCONJ
ejpam-3703	74	2	s	s	PROPN
ejpam-3703	74	3	is	be	AUX
ejpam-3703	74	4	intra	intra	ADJ
ejpam-3703	74	5	-	-	ADJ
ejpam-3703	74	6	regular	regular	ADJ
ejpam-3703	74	7	and	and	CCONJ
ejpam-3703	74	8	q	q	NOUN
ejpam-3703	74	9	∗	∗	NOUN
ejpam-3703	74	10	s	s	NOUN
ejpam-3703	74	11	is	be	AUX
ejpam-3703	74	12	a	a	DET
ejpam-3703	74	13	right	right	ADJ
ejpam-3703	74	14	ideal	ideal	NOUN
ejpam-3703	74	15	and	and	CCONJ
ejpam-3703	74	16	s	s	X
ejpam-3703	74	17	∗q	∗q	PROPN
ejpam-3703	74	18	is	be	AUX
ejpam-3703	74	19	a	a	DET
ejpam-3703	74	20	left	left	ADJ
ejpam-3703	74	21	ideal	ideal	NOUN
ejpam-3703	74	22	of	of	ADP
ejpam-3703	74	23	s	s	PROPN
ejpam-3703	74	24	,	,	PUNCT
ejpam-3703	74	25	by	by	ADP
ejpam-3703	74	26	lemma	lemma	PROPN
ejpam-3703	74	27	7	7	NUM
ejpam-3703	74	28	,	,	PUNCT
ejpam-3703	74	29	we	we	PRON
ejpam-3703	74	30	have	have	VERB
ejpam-3703	74	31	(	(	PUNCT
ejpam-3703	74	32	q	q	NOUN
ejpam-3703	74	33	∗	∗	NUM
ejpam-3703	74	34	s	s	NOUN
ejpam-3703	74	35	)	)	PUNCT
ejpam-3703	74	36	∩	∩	NOUN
ejpam-3703	74	37	(	(	PUNCT
ejpam-3703	74	38	s	s	PROPN
ejpam-3703	74	39	∗q	∗q	PROPN
ejpam-3703	74	40	)	)	PUNCT
ejpam-3703	74	41	⊆	⊆	NUM
ejpam-3703	74	42	(	(	PUNCT
ejpam-3703	74	43	s	s	X
ejpam-3703	74	44	∗q	∗q	PROPN
ejpam-3703	74	45	)	)	PUNCT
ejpam-3703	74	46	∗	∗	NOUN
ejpam-3703	74	47	(	(	PUNCT
ejpam-3703	74	48	q	q	NOUN
ejpam-3703	74	49	∗	∗	NOUN
ejpam-3703	74	50	s	s	NOUN
ejpam-3703	74	51	)	)	PUNCT
ejpam-3703	74	52	.	.	PUNCT
ejpam-3703	75	1	thus	thus	ADV
ejpam-3703	75	2	we	we	PRON
ejpam-3703	75	3	have	have	VERB
ejpam-3703	75	4	q	q	NOUN
ejpam-3703	75	5	=	=	PUNCT
ejpam-3703	75	6	(	(	PUNCT
ejpam-3703	75	7	q	q	NOUN
ejpam-3703	75	8	∗	∗	X
ejpam-3703	75	9	s	s	NOUN
ejpam-3703	75	10	)	)	PUNCT
ejpam-3703	75	11	∗	∗	NOUN
ejpam-3703	75	12	(	(	PUNCT
ejpam-3703	75	13	q	q	NOUN
ejpam-3703	75	14	∗	∗	X
ejpam-3703	75	15	s	s	NOUN
ejpam-3703	75	16	)	)	PUNCT
ejpam-3703	75	17	∗	∗	NOUN
ejpam-3703	75	18	(	(	PUNCT
ejpam-3703	75	19	s	s	X
ejpam-3703	75	20	∗q	∗q	PROPN
ejpam-3703	75	21	)	)	PUNCT
ejpam-3703	75	22	∗	∗	NOUN
ejpam-3703	75	23	(	(	PUNCT
ejpam-3703	75	24	s	s	X
ejpam-3703	75	25	∗q	∗q	PROPN
ejpam-3703	75	26	)	)	PUNCT
ejpam-3703	75	27	⊆	⊆	NUM
ejpam-3703	75	28	(	(	PUNCT
ejpam-3703	75	29	q	q	NOUN
ejpam-3703	75	30	∗	∗	NUM
ejpam-3703	75	31	s	s	NOUN
ejpam-3703	75	32	)	)	PUNCT
ejpam-3703	75	33	∗	∗	NOUN
ejpam-3703	75	34	(	(	PUNCT
ejpam-3703	75	35	s	s	X
ejpam-3703	75	36	∗q	∗q	PROPN
ejpam-3703	75	37	)	)	PUNCT
ejpam-3703	75	38	∗	∗	NOUN
ejpam-3703	75	39	(	(	PUNCT
ejpam-3703	75	40	q	q	NOUN
ejpam-3703	75	41	∗	∗	X
ejpam-3703	75	42	s	s	NOUN
ejpam-3703	75	43	)	)	PUNCT
ejpam-3703	75	44	∗	∗	NOUN
ejpam-3703	75	45	(	(	PUNCT
ejpam-3703	75	46	s	s	X
ejpam-3703	75	47	∗q	∗q	PROPN
ejpam-3703	75	48	)	)	PUNCT
ejpam-3703	75	49	=	=	PUNCT
ejpam-3703	76	1	(	(	PUNCT
ejpam-3703	76	2	q	q	NOUN
ejpam-3703	76	3	∗	∗	X
ejpam-3703	76	4	s	s	NOUN
ejpam-3703	76	5	∗	∗	NOUN
ejpam-3703	76	6	s	s	PART
ejpam-3703	76	7	∗q	∗q	NOUN
ejpam-3703	76	8	)	)	PUNCT
ejpam-3703	76	9	∗	∗	NOUN
ejpam-3703	76	10	(	(	PUNCT
ejpam-3703	76	11	q	q	NOUN
ejpam-3703	76	12	∗	∗	NOUN
ejpam-3703	76	13	s	s	NOUN
ejpam-3703	76	14	∗	∗	NOUN
ejpam-3703	76	15	s	s	PART
ejpam-3703	76	16	∗q	∗q	NOUN
ejpam-3703	76	17	)	)	PUNCT
ejpam-3703	76	18	=	=	PUNCT
ejpam-3703	77	1	(	(	PUNCT
ejpam-3703	77	2	q	q	NOUN
ejpam-3703	77	3	∗	∗	X
ejpam-3703	77	4	s	s	PART
ejpam-3703	77	5	∗q	∗q	NOUN
ejpam-3703	77	6	)	)	PUNCT
ejpam-3703	77	7	∗	∗	NOUN
ejpam-3703	77	8	(	(	PUNCT
ejpam-3703	77	9	q	q	NOUN
ejpam-3703	77	10	∗	∗	X
ejpam-3703	77	11	s	s	PART
ejpam-3703	77	12	∗q	∗q	NOUN
ejpam-3703	77	13	)	)	PUNCT
ejpam-3703	77	14	(	(	PUNCT
ejpam-3703	77	15	by	by	ADP
ejpam-3703	77	16	lemma	lemma	PROPN
ejpam-3703	77	17	5	5	NUM
ejpam-3703	77	18	)	)	PUNCT
ejpam-3703	77	19	=	=	PUNCT
ejpam-3703	77	20	q	q	PROPN
ejpam-3703	77	21	∗q	∗q	PROPN
ejpam-3703	77	22	⊆	⊆	NUM
ejpam-3703	77	23	(	(	PUNCT
ejpam-3703	77	24	q	q	NOUN
ejpam-3703	77	25	∗	∗	NUM
ejpam-3703	77	26	s	s	NOUN
ejpam-3703	77	27	)	)	PUNCT
ejpam-3703	77	28	∩	∩	NOUN
ejpam-3703	77	29	(	(	PUNCT
ejpam-3703	77	30	s	s	PROPN
ejpam-3703	77	31	∗q	∗q	NOUN
ejpam-3703	77	32	)	)	PUNCT
ejpam-3703	77	33	⊆	⊆	NUM
ejpam-3703	77	34	q	q	NOUN
ejpam-3703	77	35	,	,	PUNCT
ejpam-3703	77	36	and	and	CCONJ
ejpam-3703	77	37	q	q	ADJ
ejpam-3703	77	38	∗q	∗q	PROPN
ejpam-3703	77	39	=	=	SYM
ejpam-3703	77	40	q.	q.	PROPN
ejpam-3703	77	41	hence	hence	ADV
ejpam-3703	77	42	(	(	PUNCT
ejpam-3703	77	43	q	q	INTJ
ejpam-3703	77	44	,	,	PUNCT
ejpam-3703	77	45	∗	∗	NOUN
ejpam-3703	77	46	)	)	PUNCT
ejpam-3703	77	47	is	be	AUX
ejpam-3703	77	48	an	an	DET
ejpam-3703	77	49	idempotent	idempotent	ADJ
ejpam-3703	77	50	semigroup	semigroup	NOUN
ejpam-3703	77	51	and	and	CCONJ
ejpam-3703	77	52	so	so	ADV
ejpam-3703	77	53	is	be	AUX
ejpam-3703	77	54	a	a	DET
ejpam-3703	77	55	band	band	NOUN
ejpam-3703	77	56	.	.	PUNCT
ejpam-3703	78	1	⇐	⇐	PROPN
ejpam-3703	78	2	=	=	PRON
ejpam-3703	78	3	.	.	PUNCT
ejpam-3703	79	1	let	let	VERB
ejpam-3703	79	2	a	a	PRON
ejpam-3703	79	3	be	be	AUX
ejpam-3703	79	4	a	a	DET
ejpam-3703	79	5	right	right	ADJ
ejpam-3703	79	6	ideal	ideal	NOUN
ejpam-3703	79	7	and	and	CCONJ
ejpam-3703	79	8	b	b	DET
ejpam-3703	79	9	a	a	DET
ejpam-3703	79	10	left	left	ADJ
ejpam-3703	79	11	ideal	ideal	NOUN
ejpam-3703	79	12	of	of	ADP
ejpam-3703	79	13	s.	s.	PROPN
ejpam-3703	79	14	by	by	ADP
ejpam-3703	79	15	lemma	lemma	PROPN
ejpam-3703	79	16	3	3	NUM
ejpam-3703	79	17	,	,	PUNCT
ejpam-3703	79	18	a∩b	a∩b	PROPN
ejpam-3703	79	19	is	be	AUX
ejpam-3703	79	20	a	a	DET
ejpam-3703	79	21	quasi	quasi	NOUN
ejpam-3703	79	22	-	-	NOUN
ejpam-3703	79	23	ideal	ideal	NOUN
ejpam-3703	79	24	of	of	ADP
ejpam-3703	79	25	s.	s.	PROPN
ejpam-3703	79	26	by	by	ADP
ejpam-3703	79	27	hypothesis	hypothesis	NOUN
ejpam-3703	79	28	,	,	PUNCT
ejpam-3703	79	29	we	we	PRON
ejpam-3703	79	30	have	have	VERB
ejpam-3703	79	31	a∩b	a∩b	NOUN
ejpam-3703	79	32	=	=	SYM
ejpam-3703	79	33	(	(	PUNCT
ejpam-3703	79	34	a∩b)∗(a∩b	a∩b)∗(a∩b	PROPN
ejpam-3703	79	35	)	)	PUNCT
ejpam-3703	79	36	⊆	⊆	NUM
ejpam-3703	79	37	a∗b	a∗b	NUM
ejpam-3703	79	38	,	,	PUNCT
ejpam-3703	79	39	b	b	NOUN
ejpam-3703	79	40	∗a	∗a	PROPN
ejpam-3703	79	41	.	.	PUNCT
ejpam-3703	80	1	since	since	SCONJ
ejpam-3703	80	2	a∩b	a∩b	PROPN
ejpam-3703	80	3	⊆	⊆	NUM
ejpam-3703	80	4	a∗b	a∗b	NUM
ejpam-3703	80	5	,	,	PUNCT
ejpam-3703	80	6	by	by	ADP
ejpam-3703	80	7	lemma	lemma	PROPN
ejpam-3703	80	8	4	4	NUM
ejpam-3703	80	9	,	,	PUNCT
ejpam-3703	80	10	s	s	VERB
ejpam-3703	80	11	is	be	AUX
ejpam-3703	80	12	regular	regular	ADJ
ejpam-3703	80	13	.	.	PUNCT
ejpam-3703	81	1	since	since	SCONJ
ejpam-3703	81	2	a	a	DET
ejpam-3703	81	3	∩b	∩b	NOUN
ejpam-3703	81	4	⊆	⊆	NUM
ejpam-3703	81	5	b	b	NOUN
ejpam-3703	81	6	∗a	∗a	PROPN
ejpam-3703	81	7	,	,	PUNCT
ejpam-3703	81	8	by	by	ADP
ejpam-3703	81	9	lemma	lemma	PROPN
ejpam-3703	81	10	7	7	NUM
ejpam-3703	81	11	,	,	PUNCT
ejpam-3703	81	12	s	s	VERB
ejpam-3703	81	13	is	be	AUX
ejpam-3703	81	14	intra	intra	ADJ
ejpam-3703	81	15	-	-	ADJ
ejpam-3703	81	16	regular	regular	ADJ
ejpam-3703	81	17	.	.	PUNCT
ejpam-3703	82	1	�	�	PROPN
ejpam-3703	82	2	corollary	corollary	NOUN
ejpam-3703	82	3	9	9	NUM
ejpam-3703	82	4	an	an	DET
ejpam-3703	82	5	hypersemigroup	hypersemigroup	NOUN
ejpam-3703	82	6	(	(	PUNCT
ejpam-3703	82	7	s	s	NOUN
ejpam-3703	82	8	,	,	PUNCT
ejpam-3703	82	9	◦	◦	NOUN
ejpam-3703	82	10	)	)	PUNCT
ejpam-3703	82	11	is	be	AUX
ejpam-3703	82	12	both	both	CCONJ
ejpam-3703	82	13	regular	regular	ADJ
ejpam-3703	82	14	and	and	CCONJ
ejpam-3703	82	15	intra	intra	ADJ
ejpam-3703	82	16	-	-	ADJ
ejpam-3703	82	17	regular	regular	ADJ
ejpam-3703	82	18	if	if	SCONJ
ejpam-3703	82	19	and	and	CCONJ
ejpam-3703	82	20	only	only	ADV
ejpam-3703	82	21	if	if	SCONJ
ejpam-3703	82	22	the	the	DET
ejpam-3703	82	23	set	set	NOUN
ejpam-3703	82	24	q	q	NOUN
ejpam-3703	82	25	of	of	ADP
ejpam-3703	82	26	all	all	DET
ejpam-3703	82	27	quasi	quasi	NOUN
ejpam-3703	82	28	-	-	NOUN
ejpam-3703	82	29	ideals	ideal	NOUN
ejpam-3703	82	30	of	of	ADP
ejpam-3703	82	31	s	s	NOUN
ejpam-3703	82	32	with	with	ADP
ejpam-3703	82	33	the	the	DET
ejpam-3703	82	34	operation	operation	NOUN
ejpam-3703	82	35	“	"	PUNCT
ejpam-3703	82	36	∗	∗	NOUN
ejpam-3703	82	37	”	"	PUNCT
ejpam-3703	82	38	is	be	AUX
ejpam-3703	82	39	a	a	DET
ejpam-3703	82	40	band	band	NOUN
ejpam-3703	82	41	.	.	PUNCT
ejpam-3703	83	1	proof	proof	NOUN
ejpam-3703	83	2	if	if	SCONJ
ejpam-3703	83	3	(	(	PUNCT
ejpam-3703	83	4	q	q	NOUN
ejpam-3703	83	5	,	,	PUNCT
ejpam-3703	83	6	∗	∗	NOUN
ejpam-3703	83	7	)	)	PUNCT
ejpam-3703	83	8	is	be	AUX
ejpam-3703	83	9	a	a	DET
ejpam-3703	83	10	band	band	NOUN
ejpam-3703	83	11	,	,	PUNCT
ejpam-3703	83	12	that	that	PRON
ejpam-3703	83	13	is	be	AUX
ejpam-3703	83	14	an	an	DET
ejpam-3703	83	15	idempotent	idempotent	ADJ
ejpam-3703	83	16	semigroup	semigroup	NOUN
ejpam-3703	83	17	,	,	PUNCT
ejpam-3703	83	18	then	then	ADV
ejpam-3703	83	19	for	for	ADP
ejpam-3703	83	20	every	every	PRON
ejpam-3703	83	21	q	q	PROPN
ejpam-3703	83	22	∈	∈	PROPN
ejpam-3703	83	23	q	q	NOUN
ejpam-3703	83	24	,	,	PUNCT
ejpam-3703	83	25	we	we	PRON
ejpam-3703	83	26	have	have	VERB
ejpam-3703	83	27	q∗q	q∗q	VERB
ejpam-3703	83	28	=	=	SYM
ejpam-3703	83	29	q	q	NOUN
ejpam-3703	83	30	,	,	PUNCT
ejpam-3703	83	31	that	that	PRON
ejpam-3703	83	32	means	mean	VERB
ejpam-3703	83	33	that	that	SCONJ
ejpam-3703	83	34	the	the	DET
ejpam-3703	83	35	quasi	quasi	NOUN
ejpam-3703	83	36	-	-	NOUN
ejpam-3703	83	37	ideals	ideal	NOUN
ejpam-3703	83	38	of	of	ADP
ejpam-3703	83	39	(	(	PUNCT
ejpam-3703	83	40	s	s	X
ejpam-3703	83	41	,	,	PUNCT
ejpam-3703	83	42	◦	◦	NOUN
ejpam-3703	83	43	)	)	PUNCT
ejpam-3703	83	44	are	be	AUX
ejpam-3703	83	45	idempotent	idempotent	ADJ
ejpam-3703	83	46	so	so	ADV
ejpam-3703	83	47	,	,	PUNCT
ejpam-3703	83	48	by	by	ADP
ejpam-3703	83	49	theorem	theorem	NOUN
ejpam-3703	83	50	8	8	NUM
ejpam-3703	83	51	,	,	PUNCT
ejpam-3703	83	52	s	s	VERB
ejpam-3703	83	53	is	be	AUX
ejpam-3703	83	54	both	both	PRON
ejpam-3703	83	55	regular	regular	ADJ
ejpam-3703	83	56	and	and	CCONJ
ejpam-3703	83	57	intra	intra	ADJ
ejpam-3703	83	58	-	-	ADJ
ejpam-3703	83	59	regular	regular	ADJ
ejpam-3703	83	60	.	.	PUNCT
ejpam-3703	84	1	�	�	PROPN
ejpam-3703	84	2	references	reference	VERB
ejpam-3703	84	3	350	350	NUM
ejpam-3703	84	4	references	reference	NOUN
ejpam-3703	84	5	[	[	X
ejpam-3703	84	6	1	1	NUM
ejpam-3703	84	7	]	]	X
ejpam-3703	84	8	a.h	a.h	PROPN
ejpam-3703	84	9	.	.	PROPN
ejpam-3703	84	10	clifford	clifford	PROPN
ejpam-3703	84	11	,	,	PUNCT
ejpam-3703	84	12	g.b	g.b	PROPN
ejpam-3703	84	13	.	.	PROPN
ejpam-3703	84	14	preston	preston	PROPN
ejpam-3703	84	15	.	.	PUNCT
ejpam-3703	85	1	the	the	DET
ejpam-3703	85	2	algebraic	algebraic	PROPN
ejpam-3703	85	3	theory	theory	NOUN
ejpam-3703	85	4	of	of	ADP
ejpam-3703	85	5	semigroups	semigroup	NOUN
ejpam-3703	85	6	.	.	PUNCT
ejpam-3703	86	1	vol	vol	NOUN
ejpam-3703	86	2	.	.	PUNCT
ejpam-3703	86	3	i.	i.	PROPN
ejpam-3703	86	4	mathematical	mathematical	PROPN
ejpam-3703	86	5	surveys	survey	NOUN
ejpam-3703	86	6	,	,	PUNCT
ejpam-3703	86	7	no	no	INTJ
ejpam-3703	86	8	.	.	NOUN
ejpam-3703	86	9	7	7	NUM
ejpam-3703	86	10	american	american	PROPN
ejpam-3703	86	11	mathematical	mathematical	ADJ
ejpam-3703	86	12	society	society	NOUN
ejpam-3703	86	13	,	,	PUNCT
ejpam-3703	86	14	providence	providence	NOUN
ejpam-3703	86	15	,	,	PUNCT
ejpam-3703	86	16	r.i	r.i	PROPN
ejpam-3703	86	17	.	.	PROPN
ejpam-3703	86	18	1961	1961	NUM
ejpam-3703	86	19	.	.	PUNCT
ejpam-3703	87	1	[	[	X
ejpam-3703	87	2	2	2	NUM
ejpam-3703	87	3	]	]	PUNCT
ejpam-3703	87	4	n.	n.	NOUN
ejpam-3703	87	5	kehayopulu	kehayopulu	PROPN
ejpam-3703	87	6	.	.	PUNCT
ejpam-3703	88	1	on	on	ADP
ejpam-3703	88	2	regular	regular	ADJ
ejpam-3703	88	3	le	le	X
ejpam-3703	88	4	-	-	PUNCT
ejpam-3703	88	5	semigroups	semigroup	NOUN
ejpam-3703	88	6	.	.	PUNCT
ejpam-3703	89	1	semigroup	semigroup	PROPN
ejpam-3703	89	2	forum	forum	PROPN
ejpam-3703	89	3	49(2):267–269	49(2):267–269	PROPN
ejpam-3703	89	4	,	,	PUNCT
ejpam-3703	89	5	1994	1994	NUM
ejpam-3703	89	6	.	.	PUNCT
ejpam-3703	90	1	[	[	X
ejpam-3703	90	2	3	3	X
ejpam-3703	90	3	]	]	X
ejpam-3703	90	4	n.	n.	NOUN
ejpam-3703	90	5	kehayopulu	kehayopulu	PROPN
ejpam-3703	90	6	.	.	PUNCT
ejpam-3703	91	1	on	on	ADP
ejpam-3703	91	2	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	91	3	.	.	PUNCT
ejpam-3703	92	1	pure	pure	ADJ
ejpam-3703	92	2	mathematics	mathematic	NOUN
ejpam-3703	92	3	and	and	CCONJ
ejpam-3703	92	4	applications	application	NOUN
ejpam-3703	92	5	(	(	PUNCT
ejpam-3703	92	6	pu.m.a	pu.m.a	PROPN
ejpam-3703	92	7	.	.	PUNCT
ejpam-3703	92	8	)	)	PUNCT
ejpam-3703	93	1	25(2):151–156	25(2):151–156	PROPN
ejpam-3703	93	2	,	,	PUNCT
ejpam-3703	93	3	2015	2015	NUM
ejpam-3703	93	4	.	.	PUNCT
ejpam-3703	94	1	[	[	X
ejpam-3703	94	2	4	4	X
ejpam-3703	94	3	]	]	PUNCT
ejpam-3703	94	4	n.kehayopulu	n.kehayopulu	NUM
ejpam-3703	94	5	.	.	PUNCT
ejpam-3703	94	6	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	94	7	and	and	CCONJ
ejpam-3703	94	8	fuzzy	fuzzy	ADJ
ejpam-3703	94	9	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	94	10	.	.	PUNCT
ejpam-3703	95	1	european	european	ADJ
ejpam-3703	95	2	journal	journal	PROPN
ejpam-3703	95	3	of	of	ADP
ejpam-3703	95	4	pure	pure	ADJ
ejpam-3703	95	5	and	and	CCONJ
ejpam-3703	95	6	applied	apply	VERB
ejpam-3703	95	7	mathematics	mathematic	NOUN
ejpam-3703	95	8	10(5):929–945	10(5):929–945	NUM
ejpam-3703	95	9	,	,	PUNCT
ejpam-3703	95	10	2017	2017	NUM
ejpam-3703	95	11	.	.	PUNCT
ejpam-3703	96	1	[	[	X
ejpam-3703	96	2	5	5	X
ejpam-3703	96	3	]	]	PUNCT
ejpam-3703	96	4	n.	n.	NOUN
ejpam-3703	96	5	kehayopulu	kehayopulu	PROPN
ejpam-3703	96	6	.	.	PUNCT
ejpam-3703	97	1	how	how	SCONJ
ejpam-3703	97	2	we	we	PRON
ejpam-3703	97	3	pass	pass	VERB
ejpam-3703	97	4	from	from	ADP
ejpam-3703	97	5	semigroups	semigroup	NOUN
ejpam-3703	97	6	to	to	ADP
ejpam-3703	97	7	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	97	8	.	.	PUNCT
ejpam-3703	98	1	lobachevskii	lobachevskii	PROPN
ejpam-3703	98	2	journal	journal	PROPN
ejpam-3703	98	3	of	of	ADP
ejpam-3703	98	4	mathematics	mathematics	PROPN
ejpam-3703	98	5	39(1):121–128	39(1):121–128	PROPN
ejpam-3703	98	6	,	,	PUNCT
ejpam-3703	98	7	2018	2018	NUM
ejpam-3703	98	8	.	.	PUNCT
ejpam-3703	99	1	[	[	X
ejpam-3703	99	2	6	6	NUM
ejpam-3703	99	3	]	]	X
ejpam-3703	99	4	n.	n.	NOUN
ejpam-3703	99	5	kehayopulu	kehayopulu	PROPN
ejpam-3703	99	6	.	.	PUNCT
ejpam-3703	100	1	from	from	ADP
ejpam-3703	100	2	ordered	order	VERB
ejpam-3703	100	3	semigroups	semigroup	NOUN
ejpam-3703	100	4	to	to	PART
ejpam-3703	100	5	ordered	order	VERB
ejpam-3703	100	6	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	100	7	.	.	PUNCT
ejpam-3703	101	1	turkish	turkish	ADJ
ejpam-3703	101	2	journal	journal	NOUN
ejpam-3703	101	3	of	of	ADP
ejpam-3703	101	4	mathematics	mathematic	NOUN
ejpam-3703	101	5	43(1):21–35	43(1):21–35	NUM
ejpam-3703	101	6	,	,	PUNCT
ejpam-3703	101	7	2019	2019	NUM
ejpam-3703	101	8	.	.	PUNCT
ejpam-3703	102	1	[	[	X
ejpam-3703	102	2	7	7	X
ejpam-3703	102	3	]	]	X
ejpam-3703	102	4	n.	n.	NOUN
ejpam-3703	102	5	kehayopulu	kehayopulu	PROPN
ejpam-3703	102	6	.	.	PUNCT
ejpam-3703	103	1	lattice	lattice	PROPN
ejpam-3703	103	2	ordered	order	VERB
ejpam-3703	103	3	semigroups	semigroup	NOUN
ejpam-3703	103	4	and	and	CCONJ
ejpam-3703	103	5	hypersemigroups	hypersemigroup	NOUN
ejpam-3703	103	6	.	.	PUNCT
ejpam-3703	104	1	turkish	turkish	ADJ
ejpam-3703	104	2	journal	journal	NOUN
ejpam-3703	104	3	of	of	ADP
ejpam-3703	104	4	mathematics	mathematics	PROPN
ejpam-3703	104	5	43(5):2592–2601	43(5):2592–2601	NUM
ejpam-3703	104	6	,	,	PUNCT
ejpam-3703	104	7	2019	2019	NUM
ejpam-3703	104	8	.	.	PUNCT
ejpam-3703	105	1	[	[	X
ejpam-3703	105	2	8	8	NUM
ejpam-3703	105	3	]	]	PUNCT
ejpam-3703	105	4	m.	m.	NOUN
ejpam-3703	105	5	petrich	petrich	PROPN
ejpam-3703	105	6	.	.	PUNCT
ejpam-3703	106	1	introduction	introduction	NOUN
ejpam-3703	106	2	to	to	ADP
ejpam-3703	106	3	semigroups	semigroup	NOUN
ejpam-3703	106	4	.	.	PUNCT
ejpam-3703	107	1	merrill	merrill	NOUN
ejpam-3703	107	2	research	research	NOUN
ejpam-3703	107	3	and	and	CCONJ
ejpam-3703	107	4	lecture	lecture	NOUN
ejpam-3703	107	5	series	series	NOUN
ejpam-3703	107	6	.	.	PUNCT
ejpam-3703	108	1	charles	charles	PROPN
ejpam-3703	108	2	e.	e.	PROPN
ejpam-3703	108	3	merrill	merrill	PROPN
ejpam-3703	108	4	publishing	publishing	PROPN
ejpam-3703	108	5	co.	co.	PROPN
ejpam-3703	108	6	,	,	PUNCT
ejpam-3703	108	7	columbus	columbus	PROPN
ejpam-3703	108	8	,	,	PUNCT
ejpam-3703	108	9	ohio	ohio	PROPN
ejpam-3703	108	10	1973	1973	NUM
ejpam-3703	108	11	.	.	PUNCT